Question

A man is standing on the deck of a ship, which is 8 m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. Calculate the distance of the hill from the ship and the height of the hill.

Answer 1

Let H be the height of hill CE and a man is standing on a ship at the height of 8 meter above from the water level.

Let AB = 8, BC = x, AD = BC, AB = DC, DE = h. 

∠ACB = 30° and ∠DAE = 60°

We have to find x and H

The corresponding figure is as follows

In ΔABC

⇒ `tan 30^circ = 8/x`

⇒ `1/sqrt(3) = 8/x`

⇒ `x = 8sqrt(3)`

Again in ΔDAE,

⇒ `tan 60^circ = h/x`

⇒ `sqrt(3) = h/x`

⇒ `h = xsqrt(3)`

⇒ h = 24

Therefore, H = h + 8

⇒ H = 24 + 8

⇒ H = 32

Hence, the required distance is `8sqrt(3)` m and height is 32 m.