Question

An observer 1.5 m tall is 28.5 m away from a tower and the angle of elevation of the top of the tower from the eye of the observer is 45°. The height of the tower is ______.

Options

• 27 m

• 30 m

• 28.5 m

• none of these

Answer 1

An observer 1.5 m tall is 28.5 m away from a tower and the angle of elevation of the top of the tower from the eye of the observer is 45°. The height of the tower is 30 m.

Explanation:

Let AB be the observer and CD = h metres be the tower.

BE = AC = 28.5 m.

From right ΔBED, we have

`(DE)/(BE) = tan 45^circ`

⇒ `(DE)/(28.5  m) = 1`

⇒ DE = 28.5 m

∴ h – 1.5 = 28.5

⇒ h = 30