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Question

A man rowing a boat away from a lighthouse which is 100 m high takes 2 min to change the angle of elevation of the light house from 45 to 30. The speed of the boat is [Tan 45=1, Tan 30 = 0.57]


A

26.7 m /min

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B

37.7 m /min

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C

75.4 m /min

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D

47.4 m /min

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Solution

The correct option is B

37.7 m /min


Let the lighthouse AB=100 m and boat moves from C to D

In ABCTan 45=100CB=1 CB=100 m

In ADBTan 30=100DB=0.57 DB=1000.57=175.4 mCD=BDBCCD=175.4100=75.4It takes 2 min to move from C to DSpeed=DistanceTime=75.42=37.7m/min


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