# 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.

To find: height of the tower.

Formula Used:

Explanation:

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) = cot θ)

h = 9 (cot θ) ….. (2)

9 = 4 tan2θ

tan θ = 3/2

putting value of tan θ in 1

Height of tower

= 6m

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