Two poles are ‘a’ metres apart and the height of one is double of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the smaller is

Question

Philoid · Accepted Answer

Let AB and CD be the two poles of height h meters and 2h meters respectively such that BD be a km i.e.; the distance between the two poles and P be the midpoint of BD .

Given ∠APB = θ and ∠CPD = 90 – θ

In Δ ABP

tan θ =

tan θ = …………………1

In Δ CDP

cot (90° – θ) = PD / CD =

cot (90° – θ )=

tan θ = ………….2

Equating 1 and 2

=

8 h ² = a²

h = m