Q. 624.6( 11 Votes )

From the top of a light house, the angles of depression of two ships on the opposite sides of it are observed to be α and β. If the height of the light house be h metres and the line joining the ships passes through the foot of the light house, show that the distance between the ship is

Answer :

In the fig AB is the light house of height h (m)


In ∆ADC


tan β =


tan β =


h = y tan β or y = ………………..(1)


In ∆ADB


tan α =


tan α =


h = x tan α or x = …………….(2)



The distance between the two ships is BC = x + y


On adding eqn (1) & (2) we get,


x + y = +



meters PROVED


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