Question

The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of depression from the top of the tower of the foot of the hill is 30°. If the tower is 50 m high, the height of the hill is ______.

Options

• 150 m

• 120 m

• 100 m

• 75 m

Answer 1

The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of depression from the top of the tower of the foot of the hill is 30°. If the tower is 50 m high, the height of the hill is 150 m.

Explanation:

Let BD = x be the horizontal distance between the tower and the hill.

From the top of the tower height 50 m the angle of depression to the foot of the hill is 30°. 

So, `tan 30^circ = 50/x`

⇒ `x = 50sqrt(3)`

At the foot of the tower the angle of elevation to the top of the hill is 60°.

So, `tan 60^circ = h/x`

⇒ `h = sqrt(3) xx x`

= `sqrt(3) xx (50sqrt(3))`

= 150 m