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Question
From the top of a light house 100 m high, the angles of depression of two ships are observed as 48° and 36° respectively. Find the distance between the two ships (in the nearest metre) if:
- the ships are on the same side of the light house,
- the ships are on the opposite sides of the light house.
Solution
Let AB the light house.
Let the two ship be C and D such that ∠ADB = 36° and ∠ACB = 48°
In ΔABC,
`(AB)/(BC) = tan 48^circ`
`=> BC = 100/(1.1106) = 90.04 m `
In ΔABD,
`(AB)/(BD) = tan 36^circ`
`=> BD = 100/ 0.7265 = 137.64 m`
i. If the ships are on the same side of the light house, then distance between the two ships = BD – BC = 48 m
ii. If the ships are on the opposite side of the light house, then distance between the two ships = BD + BC = 228 m.
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