Q. 154.3( 337 Votes )

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 :

The diagram is:

Let AB is the tower and AD is the highway.

Now from triangle ADB,

      tan 30° = AB/AD

⇒ 1/√3 = AB/AD

⇒ AB = AD/√3    .............(1)

Again from triangle ACB

      tan 60° = AB/AC

⇒ √3 = AB/AC

⇒ AB = AC√3   ........(2)

from equation 1 and 2

AD/√3 = AC√3

⇒ (DC + CA)/√3 = AC√3

⇒ DC + CA = AC√3×√3

⇒ DC + CA = 3AC

⇒ 3AC - Ac = CD

⇒ 2AC = CD

⇒ AC = CD/2 

Since time taken by car to cover CD = 6 Second

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

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