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Question

# A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min, for the angle of depression of the car to change from 30o to 45o; then after this, the time taken(in min) by the car to reach the foot of the tower, is?

A
9(1+3)
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B
92(131)
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C
18(1+3)
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D
18(31)
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Solution

## The correct option is A 9(1+√3)Given, ∠HOA=30∘ and ∠HOB=45∘. Let OH=h, thentan(∠HOA)=HAh or HA=h×tan30∘tan(∠HOB)=HBh or HB=h×tan45∘ It takes 18 mins to travel distance AB, hence speed =HB−HA18=h−(h/√3)18Time taken to travel HA = HAspeed=h√3(h−h√3)18 = 18×√3√3(√3−1) = 9(√3+1)Option A is correct.

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