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Question

# A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it If it takes 12 minutes for the angle of depression to change from 300 to 450 how soon after this will the car reach the observation tower?

A
14 min. 35 sec.
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B
15 min. 49 sec.
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C
16 min. 23 sec.
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D
18 min. 5 sec.
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Solution

## The correct option is B 16 min. 23 sec.Let AB be the tower and C and D be the point of positions of two carsGiven ∠ACB=450∠ADB=300Let AB=h ,CD=x and AC=yIn ΔABCtan450=ABAD⇒1=ABAD⇒AB=AD⇒y=hIn ABDtan300=ABAD⇒1√3=hx+y⇒x+y=√3h∴x=(x+y)−y=(√3)h−h=h(√3−1)So car cover distance h(√3−1) in 12 secondsThen car cover distance h in=[12×hh(√3−1)]=120.73=16min23sec

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