# 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.

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