Q. 415.0( 5 Votes )

A man on the deck of a ship is 10 m above the water level. He observes that the angle of elevation of the top of a cliff is 45° and the angle of depression of the base is 30°. Calculate the distance of the cliff from the ship and the height of the cliff.

Answer :

In the fig. AB is the height of the cliff.


AB = AE+EB h+10


In ∆AED


tan 45° =


1 =


DE = h -----(1)


In ∆DEB


tan 30° =



DE = 10√3 -----(2)


From eqn. (1) and eqn. (2) we get,


h = 10√3



Height of cliff = AE+EB


= 10√3+10


= 27.32 m.


Therefore distance of the cliff from the ship is 10√3 and Height of cliff is 27.32m.


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