An isosceles triangle of wood of base 10 feet and height 8 3 feet is placed vertically with its base on the ground and vertex directly above. The triangle faces the sun whose altitude is 30 o . Then, the tangent of the angle at the apex of the shadow is

Question

An isosceles triangle of wood of base 10 feet and height 8 3 feet is placed vertically with its base on the ground and vertex directly above. The triangle faces the sun whose altitude is 30 o . Then, the tangent of the angle at the apex of the shadow is, 80, 80 39, 89 2, 80 217

MARKS App · Accepted Answer

Let, A B C is the triangle and triangle B C E is its shadow on the ground Height of the triangular shadow = D E = 8 3 cot ⁡ 30 o = 8 feet ∴ tan ⁡ α = 5 8 (from ∆ B D E ) tan ⁡ 2 α = 2 tan ⁡ α 1 - tan 2 ⁡ α = 2 × 5 8 1 - 25 64 = 5 4 × 64 39 = 80 39

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