Question

The angles of elevation of the top of a tower from two points at distances of 5 metres and 20 metres from the base of the tower and in the same straight line with it, are complementary. Find the height of the tower.

Answer 1

From figure: Let θ be the angle of elevation.

Given: Angle are complementary, so another angle is (90- θ)°

From right triangle CAB:

tan θ = AB/AC

tan θ = h/5

or h = 5tan θ ….(1)

Form another right triangle DAB:

tan (90-θ)° = AB/AD

tan (90-θ)° = h/20

or h = 20 tan (90-θ)°

or h = 20 cot θ …(2)

Multiply equation (1) and (2), we get

h² = 100 x tan θ x cot θ

h = 10

(As tan θ = 1/cotθ)

Height of the tower is 10 m.