Sum

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?

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#### Solution

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 = 3*h* 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.

Concept: Heights and Distances

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