Question

A vertical pole and a vertical tower are on the same level ground. From the top of the pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the foot of the tower is 30°. The height of the tower if the height of the pole is 20 m, is ______.

Options

• 40 m

• 80 m

• 160 m

• 30 m

Answer 1

A vertical pole and a vertical tower are on the same level ground. From the top of the pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the foot of the tower is 30°. The height of the tower if the height of the pole is 20 m, is 80 m.

Explanation:

Let pole height = 20 m and tower height = H.

Let horizontal distance between them = x.

From the top of the pole:

Angle of depression to the foot of the tower 30°

⇒ `tan 30^circ = 20/x`

= `1/sqrt(3)` 

⇒ `x = 20sqrt(3)`

Angle of elevation to the top of the tower 60°

⇒ `tan 60^circ = (H - 20)/x`

= `sqrt(3)` 

⇒ `H - 20 = xsqrt(3)` 

= `(20sqrt(3))(sqrt(3))` 

= 60 

So, H = 20 + 60

= 80 m