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Question
The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.
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Solution
Let PQ be the light house.
`=>` PQ = 60
`tan 60^@ = (PQ)/(AQ)`
`=> sqrt(3) = 60/(AQ)`
`=> AQ = 60/sqrt(3)`
`=> AQ = (20 xx 3)/sqrt(3)`
`=> AQ = (20 xx sqrt(3) xx sqrt(3))/sqrt(3)`
`=> AQ = 20sqrt(3) m`
In ΔPQB
`tan 45^@ = (PQ)/(QB)`
`=> 1 = 60/(QB)`
`=>` QB = 60 m
Now,
AB = AQ + QB
= `20sqrt(3) + 60`
= 20 × 1.732 + 60
= 94.64
= 95 m
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