Question

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 complementary. The
height of the tower is:​

Answer 1

Answer:

Let height of the tower be h m.

Given, the angles of elevation of the top of tower from the two points are complementary.

∴ ∠ACB = θ and ∠ADB = 90 – θ

In ∆ABC,

In ∆ABD,

∴ Height of the tower = h = 4 tan θ = 4 × = 6 m (Using (1))

Thus, the height of the tower is 6 m.