Q62 of 107 Page 12

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

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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