context
stringlengths
545
71.9k
questionsrc
stringlengths
16
10.2k
question
stringlengths
11
563
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
now , you can use the pythagorean theorem , if we give you two of the sides , to figure out the third side no matter what the third side is . so let 's do another one right over here . let 's say that our triangle looks like this .
can a exercise where the answer is rounded to one or two decimals be created ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
or , we could call it a right angle . and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle .
why does the triangle have to be a right triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so this is the square root of 36 times the square root of 3 . the principal root of 36 is 6 . so this simplifies to 6 square roots of 3 . so the length of b , you could write it as the square root of 108 , or you could say it 's equal to 6 times the square root of 3 .
how do you simplify sqrt 36 sqrt 3 into sqrt 6 sqrt 3 ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so if we think about the pythagorean theorem -- that a squared plus b squared is equal to c squared -- 12 you could view as c. this is the hypotenuse . the c squared is the hypotenuse squared . so you could say 12 is equal to c. and then we could say that these sides , it does n't matter whether you call one of them a ...
why is c the hypotenuse ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
in the last example we solved for the hypotenuse . we solved for c. so that 's why it 's always important to recognize that a squared plus b squared plus c squared , c is the length of the hypotenuse . so let 's just solve for b here .
how do you find c if it asks you ti give the radical sign ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
can you give me a few examples of real world scenarios proving the use of the pythagorean theorem ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and before i show you how to do that , let me give you one more piece of terminology . the longest side of a right triangle is the side opposite the 90 degree angle -- or opposite the right angle . so in this case it is this side right here .
is hypotenuse the opposite side of the right angle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so in this case it is this side right here . this is the longest side . and the way to figure out where that right triangle is , and kind of it opens into that longest side .
or the longest side of the triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle . now , with the pythagorean theorem , if we know two sides of a right triangle we can always figure out the third side .
why ca n't i use the trigonometry rule to figure out the hypotenuse of the triangle called ( soh cah toa ) is n't that easier ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
can you use the pythagorean theorem on triangles other than right ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
why does pythagorean theorem 1 follow theorem 2 ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and the way to figure out where that right triangle is , and kind of it opens into that longest side . that longest side is called the hypotenuse . and it 's good to know , because we 'll keep referring to it .
why is the longest side called the hypotenuse ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
now let 's see if we can simplify this a little bit . the square root of 108 . and what we could do is we could take the prime factorization of 108 and see how we can simplify this radical .
how would you find the square root of those ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
what is this ? 2 times 2 is 4 . 4 times 9 , this is 36 .
with 4^2+3^2=c^2 why could we not simple square root both sides and then simplify from there ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
can you apply the pythagorean theorem to the 3rd dimension ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
that is 16 . and 3 squared is the same thing as 3 times 3 . so that is 9 .
like a 3 dimensional pythagorean theorem ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
let me tell you what the pythagorean theorem is . so if we have a triangle , and the triangle has to be a right triangle , which means that one of the three angles in the triangle have to be 90 degrees . and you specify that it 's 90 degrees by drawing that little box right there .
how would we solve a problem if we were only given one side of the triangle and on of the angles ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
or , we could call it a right angle . and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle . now , with the pythagorean theorem , if we know two sides of a right triangle we can always figure out the third side . and before i show you how to do that , let me give y...
why the theorem always has to be a right triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
we have the right angle here . you go opposite the right angle . the longest side , the hypotenuse , is right there .
how would you find the opposite and the adjacent of a right triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
who made the pythagorean theorem ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so this is the square root of 36 times the square root of 3 . the principal root of 36 is 6 . so this simplifies to 6 square roots of 3 .
what exactly is a principal root ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
or , we could call it a right angle . and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle .
why does the triangle have to be a right triangle in order for the pythagorean theorem to work ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math .
what is the law of cosines ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
what is this ? 2 times 2 is 4 . 4 times 9 , this is 36 .
why do you power the 2 numbers you know and the unknown ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
what is the meaning of the term theorem in pythagorean theorem ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared . is equal to 12 squared .
how would we solve the problem if there is already c squared there like nine and we have to find a or b squared ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
how important is the pythagorean theorem ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
on the left-hand side we 're left with just a b squared is equal to -- now 144 minus 36 is what ? 144 minus 30 is 114 . and then you subtract 6 , is 108 . so this is going to be 108 .
why , did sal subtract 6 from 114 ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
or , we could call it a right angle . and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle . now , with the pythagorean theorem , if we know two sides of a right triangle we can always figure out the third side . and before i show you how to do that , let me give y...
does the pythagorean theorem only work if it 's a right triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
or , we could call it a right angle . and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle . now , with the pythagorean theorem , if we know two sides of a right triangle we can always figure out the third side . and before i show you how to do that , let me give y...
what if the right triangle has 2 equal sides and a hypotenuse , how do you find the perfect ratio ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
4 times 9 , this is 36 . so this is the square root of 36 times the square root of 3 . the principal root of 36 is 6 .
how can the length of a side of a triangle be the square root of a number ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle . now , with the pythagorean theorem , if we know two sides of a right triangle we can always figure out the third side . and before i show you how to do that , let me give you one more piece of terminology .
what are the other two sides of the triangle called ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
or , we could call it a right angle . and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle .
if i am given a triangle with a=3 , b=4 , c=5 , then is it necessarily a right triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so that 's what b squared is , and now we want to take the principal root , or the positive root , of both sides . and you get b is equal to the square root , the principal root , of 108 . now let 's see if we can simplify this a little bit .
if you square root the whole equation , should n't it be a+b=c ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
in the last example we solved for the hypotenuse . we solved for c. so that 's why it 's always important to recognize that a squared plus b squared plus c squared , c is the length of the hypotenuse . so let 's just solve for b here .
should a simpler version be a + b = c ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and before i show you how to do that , let me give you one more piece of terminology . the longest side of a right triangle is the side opposite the 90 degree angle -- or opposite the right angle . so in this case it is this side right here .
does the hypotenuse have to be on the opposite side of the right angle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
does the pythagorean theorm only apply to right triangles ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
let 's say a is equal to 6 . and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem .
and i also do n't understand the logic behind using an equation to find the length of b ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
and is the pythagorean theorem only used to find lengths ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so that 's what b squared is , and now we want to take the principal root , or the positive root , of both sides . and you get b is equal to the square root , the principal root , of 108 . now let 's see if we can simplify this a little bit .
and why does sal use the principle root of 108 to give to b instead of just giving b 108 ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
or , we could call it a right angle . and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle .
when using the pythagorean theorem , must the triangle be a right angle , or can it be just a triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
does the pythagorean theorem also work for rectangles ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and it 's good to know , because we 'll keep referring to it . and just so we always are good at identifying the hypotenuse , let me draw a couple of more right triangles . so let 's say i have a triangle that looks like that .
does the pythagorean theorm only work for right triangles ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so enough talk on my end . let me tell you what the pythagorean theorem is . so if we have a triangle , and the triangle has to be a right triangle , which means that one of the three angles in the triangle have to be 90 degrees . and you specify that it 's 90 degrees by drawing that little box right there .
can you use the pythagorean theorem on a different type of triangle , for example an isosceles triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so this is the square root of 36 times the square root of 3 . the principal root of 36 is 6 . so this simplifies to 6 square roots of 3 .
what is a principal root ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
in the last example we solved for the hypotenuse . we solved for c. so that 's why it 's always important to recognize that a squared plus b squared plus c squared , c is the length of the hypotenuse . so let 's just solve for b here .
do you always have to use a , b , c ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared . is equal to 12 squared .
so , if a squared + b squared = c squared , does that mean that a squared + c squared = b squared ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
what is the logic behind the pythagorean theorm ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
what is unique about a pythagorean triplet ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
where did the pythagorean theorem come from ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
now let 's see if we can simplify this a little bit . the square root of 108 . and what we could do is we could take the prime factorization of 108 and see how we can simplify this radical .
why do you have to use the square root ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
or , we could call it a right angle . and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle . now , with the pythagorean theorem , if we know two sides of a right triangle we can always figure out the third side . and before i show you how to do that , let me give y...
why do you think the pythagorean theorem only works on a right triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
in the last example we solved for the hypotenuse . we solved for c. so that 's why it 's always important to recognize that a squared plus b squared plus c squared , c is the length of the hypotenuse . so let 's just solve for b here .
is there a proper place to put a/b/c on the triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
would the pythagorean theorem work with an equilateral or obtuse triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math .
how do you rationalize a number ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
now let 's see if we can simplify this a little bit . the square root of 108 . and what we could do is we could take the prime factorization of 108 and see how we can simplify this radical .
what i mean is like figuring out that square root to 50 would be something like 5-2 ( five to the square root of two ) how do you do that ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
does n't a capital letter mean something different in the pythagorean theorem ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
or , we could call it a right angle . and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle .
is there a case that a right triangle is n't a `` 3-4-5 '' triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
or does the pythagorean theorem make that false ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so you take the principal root of both sides and you get 5 is equal to c. or , the length of the longest side is equal to 5 . now , you can use the pythagorean theorem , if we give you two of the sides , to figure out the third side no matter what the third side is . so let 's do another one right over here .
how can you use pythagorean theorem to find isosceles side lengths ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
does the pythagorean theorem only work for right triangles ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
we have the right angle here . you go opposite the right angle . the longest side , the hypotenuse , is right there .
why does the hypotenuse have to be the opposite of the right angle i know how to do the work but ca n't you just tell what it will be ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
in what ways can you apply pythagorean theorem to the world ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
or , we could call it a right angle . and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle .
is the pythagorean theorem only used for figuring out the side of an triangle only with a right triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
this is 12 , this is 6 . and the square root of 3 , well this is going to be a 1 point something something . so it 's going to be a little bit larger than 6 .
maybe i 'm missing something here ... for the second practice problem , sal is simplifying the radical ... why does he stick the last little three under a radical sign of its own ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and before i show you how to do that , let me give you one more piece of terminology . the longest side of a right triangle is the side opposite the 90 degree angle -- or opposite the right angle . so in this case it is this side right here .
how come the hypotenuse is on the opposite side of the right angle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
does the pythagorean theorem work on triangles with negative sides ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
in the last example we solved for the hypotenuse . we solved for c. so that 's why it 's always important to recognize that a squared plus b squared plus c squared , c is the length of the hypotenuse . so let 's just solve for b here .
is the hypotenuse always `` c '' ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so let 's call this c -- that side is c. let 's call this side right over here a . and let 's call this side over here b . so the pythagorean theorem tells us that a squared -- so the length of one of the shorter sides squared -- plus the length of the other shorter side squared is going to be equal to the length of th...
i thought side b = 54 why is it not 54 ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and before i show you how to do that , let me give you one more piece of terminology . the longest side of a right triangle is the side opposite the 90 degree angle -- or opposite the right angle . so in this case it is this side right here .
do you always put the longest side of a right angle first when solving ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
why does the pythagorean theorem only work on right triangles ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
how can we know that in which case should we use pythagorean theorem ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so let 's call this c -- that side is c. let 's call this side right over here a . and let 's call this side over here b . so the pythagorean theorem tells us that a squared -- so the length of one of the shorter sides squared -- plus the length of the other shorter side squared is going to be equal to the length of th...
does it matter which side is a or b ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
what is this ? 2 times 2 is 4 . 4 times 9 , this is 36 .
if a^2 *b^2= c^2 , would b^2= c^2 -a ^2 and a^2= c^2-b^2 ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
2 times 2 is 4 . 4 times 9 , this is 36 . so this is the square root of 36 times the square root of 3 .
should n't sal have put a times sign ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so 25 is equal to c squared . and we could take the positive square root of both sides . i guess , just if you look at it mathematically , it could be negative 5 as well .
why would you want to square root both sides ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so let 's say that c is equal to the length of the hypotenuse . so let 's call this c -- that side is c. let 's call this side right over here a . and let 's call this side over here b .
can the side with the question mark be c ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
how can you use the pythagorean theorem to derive the equation of a circle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so let 's say i have a triangle that looks like that . and i were to tell you that this angle right here is 90 degrees . in this situation this is the hypotenuse , because it is opposite the 90 degree angle .
is a right angle always equal to 90 degrees ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
in the last example we solved for the hypotenuse . we solved for c. so that 's why it 's always important to recognize that a squared plus b squared plus c squared , c is the length of the hypotenuse . so let 's just solve for b here .
why ca n't we use a+b=c ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
now let 's see if we can simplify this a little bit . the square root of 108 . and what we could do is we could take the prime factorization of 108 and see how we can simplify this radical .
what does the square stand for ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
in the last example we solved for the hypotenuse . we solved for c. so that 's why it 's always important to recognize that a squared plus b squared plus c squared , c is the length of the hypotenuse . so let 's just solve for b here .
is the hypotenuse always represented by the variable c ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
or , we could call it a right angle . and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle . now , with the pythagorean theorem , if we know two sides of a right triangle we can always figure out the third side .
can you only find the hypotenuse in a right triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared . is equal to 12 squared .
is there a particular reason why the numbers are squared ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
the longest side , the hypotenuse , is right there . so if we think about the pythagorean theorem -- that a squared plus b squared is equal to c squared -- 12 you could view as c. this is the hypotenuse . the c squared is the hypotenuse squared .
in this theorem 's case , can the hypotenuse ever be any other letter than c , such as a or b ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle . now , with the pythagorean theorem , if we know two sides of a right triangle we can always figure out the third side . and before i show you how to do that , let me give you one more piece of terminology .
do you always need to know at least two sides of the right triangle to put the pythagorean theorem into effect ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
let 's say a is equal to 6 . and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem .
does it matter what leg is a or b ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
now let 's see if we can simplify this a little bit . the square root of 108 . and what we could do is we could take the prime factorization of 108 and see how we can simplify this radical .
why ca n't i find a real square using the theorem ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
is the pythagorean theorem only used for right triangles ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
so let 's just solve for b here . so we get 6 squared is 36 , plus b squared , is equal to 12 squared -- this 12 times 12 -- is 144 . now we can subtract 36 from both sides of this equation .
if ab= 12 and bc = 13 , what is the area of the parallelogram ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
how come the pythagorean theorem only works for right triangles ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
that is 16 . and 3 squared is the same thing as 3 times 3 . so that is 9 .
what are some perfect angle lengths , like a 3 , 4 , 5 triangle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
in the last example we solved for the hypotenuse . we solved for c. so that 's why it 's always important to recognize that a squared plus b squared plus c squared , c is the length of the hypotenuse . so let 's just solve for b here .
is the hypotenuse always going to be c ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
was the pythagorean theorem named after pythagoras ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and then we say b -- this colored b -- is equal to question mark . and now we can apply the pythagorean theorem . a squared , which is 6 squared , plus the unknown b squared is equal to the hypotenuse squared -- is equal to c squared .
what is statement of pythagoras theorem ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and the way to figure out where that right triangle is , and kind of it opens into that longest side . that longest side is called the hypotenuse . and it 's good to know , because we 'll keep referring to it .
and if the hypotenuse is stated and you 're trying to figure out what side `` b '' would be , would you treat it like an algebraic expression ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
and it 's good to know , because we 'll keep referring to it . and just so we always are good at identifying the hypotenuse , let me draw a couple of more right triangles . so let 's say i have a triangle that looks like that .
does pythgorean theorem only work for right triangles ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
we have the right angle here . you go opposite the right angle . the longest side , the hypotenuse , is right there .
how is it possible that the hypotenuse is always opposite of the right angle ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
or , we could call it a right angle . and a triangle that has a right angle in it is called a right triangle . so this is called a right triangle . now , with the pythagorean theorem , if we know two sides of a right triangle we can always figure out the third side .
also he says has to be right triangle , is it possible to do it with any other kinds of triangles ?
in this video we 're going to get introduced to the pythagorean theorem , which is fun on its own . but you 'll see as you learn more and more mathematics it 's one of those cornerstone theorems of really all of math . it 's useful in geometry , it 's kind of the backbone of trigonometry . you 're also going to use it ...
that is 16 . and 3 squared is the same thing as 3 times 3 . so that is 9 .
3 , can the 3 ( a ) and the 4 ( b ) be switched around ?