An isosceles triangle made of wood of base 10 feet and height 8 feet is placed vertically with its base on the ground and vertex directly above it. If the triangle faces the sun whose altitude is 3 0 o , then the tangent of the angle at the apex of the shadow is

Question

An isosceles triangle made of wood of base 10 feet and height 8 feet is placed vertically with its base on the ground and vertex directly above it. If the triangle faces the sun whose altitude is 3 0 o , then the tangent of the angle at the apex of the shadow is, 80 3, 80 3 167, 89 2 3, 80 3 217

MARKS App · Accepted Answer

Let, A B C is the triangle and B C E is its shadow on the ground Height of the triangular shadow = D E = 8 cot ⁡ 30 o = 8 3 f e e t ∴ tan ⁡ α = 5 8 3 f r o m Δ B D E ⇒ tan ⁡ 2 α = 2 tan ⁡ α 1 - t a n 2 α = 2 5 8 3 1 - 25 192 = 5 4 3 × 192 167 = 80 3 167

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