Question

An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from her eyes is 45°. What is the height of the tower?

Options

• 20 m

• 10 m

• 40 m

• 30 m

Answer 1

30 m

Explanation:

Let AB be the tower of height h and CD be the observer of height 1.5 m at a distance of 28.5 m from the tower AB.

In ΔAED, we have

tan 45° = h/28.5

⇒ 1 = h/28.5

⇒ h = 28.5 m

∴ h = AE + BE = AE + DC

= (28.5 + 1.5) m = 30 m

Height of tower = h + 1.5

= 28.5 + 1.5

= 30 m

Hence, the height of the tower is 30 m.