Q. 70

Two ships are there in the sea on either side of a light house in such a way that the ships and the light house are in the same straight line. The angles of depression of two ships are observed from the top of the light house are 60° and 45° respectively. If the height of the light house is 200 m, find the distance between the two ships.

Answer :

In the fig AB is the light house of height of 200m.


In ∆AED


tan 45° =


1 =


x = 200m ………………….(1)


In ∆ABC


tan 60° =


√3 =


√3y = 200


y =


On multiplying and dividing by √3, we get


y = m


Therefore the distance between two ships is:



DC = x + y


x + y = 200 +



= 315.47m


Therefore the distance between two ships is 315.47m


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