Question

From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is

Options

• 25 m

• 50 m

• 75 m

•  100 m

Answer 1

Given that: height of cliff is 25 m and angle of elevation of the tower is equal to angle of depression of foot of the tower that is θ.

Now, the given situation can be represented as,

Here, D is the top of cliff and BE is the tower.

Let CE = h, `AB=x`. Then, `AB=DC`= = x 

Here, we have to find the height of the tower BE.

So, we use trigonometric ratios.

In a triangle ABD, 

`⇒ tan θ= AD/AB`

`⇒ tan θ=25/x`                  (1)

Again in a triangle,`DCE`

`tan θ=(CE)/(CD)` 

`⇒ tan θ=h/x`

`⇒25/x=h/x`              [using 1] 

`⇒h=25`

Thus, height of the tower = BE = BC + CE = (25 + 25) m = 50 m