Q. 424.1( 10 Votes )

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 :

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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