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Question
As observed from the top of a 80 m tall lighthouse, the angles of depression of two ships, on the same side of a light house in a horizontal line with its base, are 30° and 40° respectively. Find the distance between the two ships. Give your answer corrected to the nearest metre.
Solution
Let AB represent the lighthouse.
Let the two ships be at point D and C having angle of depression 30° and 40° respectively.
Let x be the distance between the two ships.
Clearly, m∠ACB = 40° and m∠ADB = 30°
In ΔACB
`tan 40^circ = 80/(CB)`
`=> CB = 80/ 0.84 = 95.24 m`
In ΔADB
`tan 30^circ = 80/(DB)`
`=> DB = 80/(0.58) = 137.93 m`
DC = DB – CB
`=>` x = 137.93 – 95.24
`=>` x = 42.69 ≈ 43 m
The distance between the two ship is 43 m.
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