If the angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complimentary, find the height of the tower.

Question

Philoid · Accepted Answer

Let the height of the tower be h meters

Given, the angles of elevation of the top of a tower from two points are complimentary

∴ ∠ACB = θ and ∠ADB = 90° - θ

In Δ ABC

tan θ = 4 / h

h = 4tan θ…………1

In ΔABD

tan (90° - θ) =

h = 9 (cot θ) ………………..( tan (90° - θ) = cot θ ) 2

cot θ = h/9

cot θ =

1/tan θ =

9 = 4 tan²θ

tan θ = 3/2

Height of tower (h)= 4 × 3/2………..putting value of tan θ in 1

= 6m