Question

From the top of a cliff 20 m high, the angle of elevation of the top 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

• 20 m

• 40 m

• 60 m

• 80 m

Answer 1

From the top of a cliff 20 m high, the angle of elevation of the top 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 40 m.

Explanation:

Let AB be the cliff and CD be the tower. Draw BE ⊥ CD.

Let ∠ACB = ∠EBD = α and let DE = h metres.

Also, AB = 20 m.

Let AC = BE = x m. 

Then, `x/h = cot α` and `x/20 = cot α`

Thus, `x/h = x/20` ⇒ h = 20.

∴ The height of the tower = (h + 20) m = 40 m.