Question

A straight highway leads to the foot of a tower. A man standing at the top of the tower
observes a car at an angle of depression of 30°, 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 60°. Find the time taken by the car to reach the foot of the tower from this point.​

Answer 1

Answer:

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Answer 2

Answer:

Let AB is the tower and BD is the highway.

Now from triangle ADB,

tan30 = AB/BD

=> 1/√3 = AB/BD

=> AB = BD/√3 .............1

Again from triangle ACB

tan60 = AB/BC

=> √3 = AB/BC

=> AB = BC√3 ........2

from equation 1 and 2

BD/√3 = BC√3

=> (BC + CD)/√3 = BC√3

=> BC + CD = BC√3*√3

=> BC + CD = 3BC

=> 3BC - BC = CD

=> 2BC = CD

=> BC = CD/2

Since time taken by car to cover CD = 6 Second

So time taken by car to cover BC = 6/2 = 3 seconds