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NationalTutoringObservatory
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MathEd-PII

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8
volunteer
It really wouldn't matter
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volunteer
Either way would be kind of a right triangle, right?
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student
Yeah
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student
OK.
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volunteer
So you're, your cameras were, we're not gonna, we're gonna assume that the camera is on the ground and it doesn't have any height.
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volunteer
right
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student
Mm
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student
Yeah
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volunteer
So we've got a little right triangle. I put it
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volunteer
on the right, the camera, but it could have been on the left.
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volunteer
and
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volunteer
at any moment in time,
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volunteer
if we think about the tangent of that angle
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volunteer
that would be
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volunteer
the way to
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volunteer
the way to try to track
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volunteer
um
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volunteer
the, the rate of change in the camera's angle.
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volunteer
We would want to come up with something like the theta DT.
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student
OK
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volunteer
Does that make sense
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student
Yeah, and then, um,
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volunteer
Well
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student
looking at it without the like data stuff, I might just assume that uh the formula for this one could be, uh, the pothagram theorem so a^2 + b^2 + c^2. Like, how did you come up with the whole data thing.
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volunteer
so what we're, we're asked for, we are asked for the rate of change of the angle, right?
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volunteer
So
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volunteer
I'm not really sure that the Pythagoras theorem
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volunteer
is, well, we'll have to see, but
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volunteer
if we could come up with a, a formula for the tangent of the angle.
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volunteer
as a function of time, then we would have it.
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volunteer
So, it may be that the Pythagorean theorem comes into play here.
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volunteer
but not necessarily.
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volunteer
um because we really can't
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volunteer
do much with the angle with the Pythagorean theorem. Do you see that?
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student
Yeah, I'm just trying to understand like when do I know to use the thagran theory and when do I need to use like tricks.
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volunteer
Right. So let's just say the problem was how fast is the distance between the rocket and the camera changing, OK?
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student
OK
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volunteer
That would be the more typical problem that you would see is, you know, the rockets going up
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volunteer
and it
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volunteer
and 5000 ft away and the rocket's traveling 600 ft per second and it's going up and up and up.
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student
Mhm
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volunteer
then definite, so if we were asked how fast is the rocket's distance changing from the camera, then we would definitely use the Pythagorean theorem.
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volunteer
to come up with that, that distance.
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student
OK
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volunteer
as a function of time. But in this case
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volunteer
they're actually focusing in on the angle, and I'm not so sure that the Pythagorean theorem is really gonna help us.
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volunteer
Uh, we may need it, but
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volunteer
if we really wanna solve the problem. I think we have to focus on the angle this time, and it may not be
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volunteer
um,
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volunteer
able to be expressed
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volunteer
with the Pythagorean theorem because that really just relates the sides of a right triangle to the hypotenuse.
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student
Oh, so like by camera angle, they mean like right here.
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volunteer
I'll mark it
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student
Wait, let me show you, like right here, right.
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volunteer
Yes, that's it, Theta. Yeah, I should, you're right, exactly.
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volunteer
So
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volunteer
yeah, because
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student
OK, now it makes sense. Since they're like showing you that small part, that's why if they're talking about this like whole line right here, then it would have been like the pathography.
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student
Yeah
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volunteer
yes, if they were saying how fast does the distance between the camera and the rocket changing, you would definitely, and that's the more typical problem that you would see.
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volunteer
Um,
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student
OK.
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volunteer
you nor more typical problem would be something like that.
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volunteer
So,
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volunteer
but it, but unfortunately or unfort unfortunately, it's not that simple when you talk about the angle, but you'll notice that
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volunteer
um with these problems, when they talk about angles, usually trying to use the tangent is pretty helpful.
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volunteer
because
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volunteer
um if we can express the tangent of that angle.
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volunteer
as a function of time that we pretty much have it
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student
Mhm.
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volunteer
So, I'm gonna think about this for a minute, but the tangent of the angle is always the opposite.
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volunteer
is always the opposite over the adjacent side, right?
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student
Yeah
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volunteer
And we know the adjacent side is always going to 5000.
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student
OK
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volunteer
feet because that's not gonna change.
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student
Yeah
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volunteer
So now the question is, can we come up with an expression for the numerator or the opposite side.
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volunteer
And we know that it started out 1000 ft.
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volunteer
So I'm thinking 1000
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volunteer
+
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volunteer
um
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volunteer
600
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volunteer
right
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volunteer
We
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volunteer
to kind of
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student
Are you writing down the board?
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student
OK
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volunteer
I will in a minute. I'm just kind of talking, talking through it right now. So I'm gonna write it on the board in a minute.
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student
OK
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student
OK.
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volunteer
Um, so let me go ahead and do that and we'll see what we think this is right. So I'm gonna go down a little further now.
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volunteer
and please stop me because, you know, there's always
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volunteer
many chances for error.
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student
OK
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volunteer
But let's go ahead here
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student
Mhm
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volunteer
tangent offain, I apologize for my handwriting. I've got a
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student
OK
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volunteer
kind of a tremor thing going on. So that's always the opposite.
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