Question
From the top of a lighthouse the angle 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 lighthouse. Show that the distance
between the ship is 
metres.
Solution
Let AD be the lighthouse whose height is h metres. 13 and C are the position of two ships which are on opposite sides of lighthouse. The angles of depression of two ships B and C from the top of the lighthouse are α and β respectively.
i.e., ∠ABD = α and ∠ACD = β
Let BD = x m and CD = y m
In right triangle ABD, we jave
In right triangle ACD, we have
Adding (i) and (ii), we get
Hence, the distance between the ship is 
metres.
