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# A straight highway leads to foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30o, which is approaching the foot of the tower with a uniform speed. Six seconds later the angle of depression of the car is found to be 60o. Find the time taken by the car to reach the foot of the tower from this point.

Asked by Topperlearning User 27th July 2017, 11:02 AM

Let PQ = h metres be the height of the tower. P is the top of the tower.

The first and second positions of the car are at A and B respectively.

APX = 30o PAQ = 30o

BPX = 60o PBQ = 60o

Let the speed of the car be x m/second

Then, distance AB = 6x meters

Let the time taken from B to Q be n seconds

BQ = nx metres

In PAQ,

...(1)

In PBQ,

...(2)

From (1) and (2),

n = 3

Hence, the time taken by the car to reach the foot of the tower from B is 3 seconds.

Answered by Expert 27th July 2017, 1:02 PM
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