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

Step-by-step solution

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