The angles of elevation of the top of a tower from two points on the ground 18 m and 32 m away from the foot of the tower are complementary. The height of the tower is:

Correct option is C

Given:

Two  points on the ground 18 m and 32 m away from the foot of the tower are complementary.

Formula Used:

 θand ϕϕare complementary:  

​tan⁡(θ)×tan⁡(ϕ)=1

Solution:

Given that the angles of elevation are complementary, we have:

θ+ϕ=90

From the two points at distances 18 m and 32 m from the foot of the tower, we can write:

tanθ =h/18

tanϕ =h/32​

Since$\theta$and$\varphi$are complementary: 

​tan⁡(θ)×tan⁡(ϕ)=1 

Substitute the values of$\tan (\theta )$and$\tan (\varphi )$:

$$\frac{h}{18}\times\frac{h}{32}=1$$

$$h^2$$​ =576

h =24m

So, height is 24m.

 ​

​

​