Question

A man 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 8meter 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 = 8/x`

`=> 1/sqrt3 = 8/x`

`=> x = 8sqrt3`

Again in  Δ DAE,

`=> tan 60^@ = h/x`

`=> sqrt3 = h/x`

`=> h = xsqrt3`

`=> h = 24`

Therefore H = h + 8`

`=> H = 24 + 8`

=> H = 32

Hence the required distance is `8sqrt3`m and height is 32 m