Question

From the top of a building 16m high, the angular elevation of top of a hill is 60° and the angle of depression of the foot of the hill is 30° . Find the height of the hill.

Answer 1

In ∆DCE , ∠CED = 30˚, DE = x

tan θ = CD/DE

tan30˚ = 16/x

1/√3 = 16/x

x = 16√3

In ∆ABC , ∠BCA = 60˚, BC = DE = x

tan θ = AB/BC

tan 60˚ = AB/x

√3 = AB/16√3

16×3 = AB

48 = AB

Therefore, the height of the hill = AB + BE = 48 + 16 = 64 m

Answer 2

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