The top of a tower makes complementary angles of elevation from two points at the distances of 25 m and 16 m from its foot on the ground. Find the height of the tower.

Correct option is C

Given:

The top of a tower makes complementary angles of elevation from two points at the distances of 25 m and 16 m from its foot on the ground. 

Formula Used: 

​$$\tan \theta = \frac{\text{Perpendiular}}{\text{Base}}=\frac{1}{\cot \theta}$$ ​

Solution:

From fig:

=> tan(90° - θ) = $$\frac{ h}{25}$$​

=> tanθ = $$\frac{h}{16}$$​

We know that => tan (90° - θ) = cotθ and cotθ = $$\frac{1}{tanθ}$$​

=>$$\frac{ 1}{\tan θ} = \frac{h}{25}$$​ ……… (eq1)

=> $$\tan θ = \frac{ h}{16}$$​ …………. (eq2)

From eq 1 and 2

=> $$\frac{ 16}h = \frac{h}{25}$$​

=> h²= 400

=> h = 20 m

Thus, height of tower is 20 meter.