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.
In the fig. AB is the height of hill AB = AE+EB ⇒ h+8
In ∆AEB
tan 60° = 
√3 = 
h = √3 DE ------- (1)
In ∆DEB
tan 30° = 
DE = 8√3 ------(2)
From eqn. (1) and eqn. (2) we get,
h = √3× 8√3 ⇒ 24 m.
Height of hill = 24+8 ⇒ 32 m.
On substitution value of h in eqn. (1)
24 = √3 DE
DE = 
DE = 
⇒ 
DE = 8√3 m.
Therefore distance between ship and hill is 8√3 m and height of the hill is 32 m.
42