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{
"id": "geo_triangle_001",
"category": "scientific",
"subcategory": "geometry",
"question": "In triangle ABC, angle A = 60°, angle B = 45°. If side AB = 10 units, find the length of side BC.",
"input_images": [],
"reasoning_steps": [
{
"step": 1,
"type": "text",
"content": "First, find angle C using the triangle angle sum property: C = 180° - 60° - 45° = 75°",
"intermediate_result": "angle C = 75°"
},
{
"step": 2,
"type": "interleaved",
"content": "Draw the triangle with labeled angles and the known side AB.",
"image_path": "images/geo_triangle_001_step2.png",
"intermediate_result": "Visual representation created"
},
{
"step": 3,
"type": "text",
"content": "Apply the Law of Sines: BC/sin(A) = AB/sin(C). Therefore BC = AB × sin(A)/sin(C) = 10 × sin(60°)/sin(75°)",
"intermediate_result": "BC = 10 × 0.866/0.966"
},
{
"step": 4,
"type": "text",
"content": "Calculate: BC = 10 × 0.866/0.966 ≈ 8.97 units",
"intermediate_result": "BC ≈ 8.97 units"
}
],
"answer": "BC ≈ 8.97 units",
"metadata": {
"difficulty": "medium",
"source": "synthetic",
"tags": ["law-of-sines", "triangle", "trigonometry"]
}
}
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