Question

A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60° and angle of depression of the base of the hill as 30°. Find the distance of the hill from the ship and the height of the hill.

Answer 1

In adjoining fig. let C represents the position of the man on the deck of the ship, A represents the top of hill and D its base. Now in right-angled triangle CWD,

Also, in right-angled triangle ABC we have,

Now, AD = AB + BD = 30 m + 10 m = 40 m.
Therefore, the distance of the hill from the ship = 17.3 m and the height of the hill = 40 m