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Question
From the top of a light house 96m high, the angles of depression of two ships in the river and at the same level as the base of the light house and on the same side of it, are α and β. If tan α = `1/4` and tan β = `1/7`, find the distance between the ships.
Solution
In the figure , TO is the light house and A and B are the position of the two ships .
In ΔAOT,
`"OT"/"OA" = tanα`
⇒ `96/"OA" = 1/4`
⇒ `"OA" = 384`
In ΔBOT,
`"OT"/"OB" = tanβ`
⇒ `96/"OB" = 1/7`
⇒ OB = 672
`therefore` Distance between the two ships = AB = OA - OB = 384 - 672 = 288 m
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