Question

The angle of elevation of the top of a tower at a point on the ground is 30º. What will be the angle of elevation, if the height of the tower is tripled?        

Answer 1

Let the height of the tower AB be h units.

Suppose C is a point on the ground such that ∠ACB=30° 

In right ∆ACB,

`tan 30°= (AB)/(AC)`

`⇒ 1/sqrt3=h/(AC)` 

`⇒ AC=sqrt3h`                  ................(1)

Let the angle of elevation of the top of the tower at C be θ, if the height of the tower is tripled.
New height of the tower, AD = 3h units 

In right ∆ACD, 

`tan θ= (AD)/(AC)` 

`⇒ tan θ =(3h)/(AC) ` 

`⇒ tan θ= (3h)/sqrt(3h)=sqrt3`           [from (1)]

`⇒ tan θ= tan 60°`

`⇒ θ=60°`

Hence, the required angle of elevation is 60º.