Q. 235.0( 4 Votes )

# 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.

Answer :

**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 tan^{2}θ

tan θ = 3/2

putting value of tan θ in 1

Height of tower

= 6m

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