Question

A boy, 1.6 m tall, is 20 m away from a tower and observes the angle of elevation of the top of the tower to be (i) 45°, (ii) 60°. Find the height of the tower in each case.

Answer 1

Let the height of the tower be h m. 

i. Here, θ = 45°

∴ `tan 45^circ = (h - 1.6 )/20`

`=> 1 = (h - 1.6)/20`

∴ h = 21.6 m

So, height of the tower is 21.6 m

ii. Here θ = 60° 

∴ `tan 60^circ = (h - 1.6)/20`

`=> sqrt(3) = (h - 1.6)/20`

∴ h = 20 × 1.732 + 1.6 = 36.24 m

So, height of the tower is 36.24 m.