Question

A man on the deck of the ship is 10 meter above water level he observes that the angle of elevation of the top of hill is 60° and the angle of depression of the base is 30° then find the distance of the hill from the ship and height of the hill

Answer 1

distance=10√ 3 , height= 40 metre will be the answer

Answer 2

Let us observe the following figure.



The point of observation is at A.

The height of the deck is 10 meters.

Thus, AB = CD = 10 meters

The top and bottom of a hill is E and C.

Therefore the angles of elevation and the depression are 

Let AD = BC = x meters.

Consider the triangle ADE.

Thus,



Now consider the triangle ABC.



Substitute the value of x from equation (2) in equation (1), we have



Therefore 

h = 30 meters  .....(4)

The height of the hill is CE

That is,



Substitute the value of h from equation (4) in equation (5), we hve



Thus, the height of the hill is 40 meters and the distance of the hill from the ship is