Question

# A man is watching from the top of a tower, a boat speeding away from the tower. The boat makes an angle of depression of 450 with the man's eye when at a distance of 60 meters from the tower. After 5 seconds the angle of depression becomes 300. What is the approximate speed of the boat assuming that it is running in still water?

A
32 kmph
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B
36 kmph
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C
38 kmph
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D
40 kmph
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E
42 kmph
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Solution

## The correct option is A 32 kmphLet AB be the tower and C and D be the point of observation from boat.Given AC=60 m and ∠ADB=300 and ∠ACB=450Let height of tower is h mIn ΔBAC,tan450=ABAC⇒1=AB60⇒AB=60 mIn ΔBAD,tan30o=ABAD⇒1√3=60AD⇒AD=60√3 m∴CD=AD−AC=60√3−60=60(√3−1)Then, speed =60(√3−1)5 m/sAnd approximate speed =12×0.73×36001000≈32 km/h

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