(29) A straight highway leads to the foot of the 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 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.

Solution:

Let AB represent the height of the tower and point

A represent the position of the man point C

and D represent position of the car

m ∠ PAC = 30°

m ∠ PAD = 60°

m∠ ACB = m∠ PAC = 30° [Alternate angles]

m∠ ADB = m∠ PAD = 60° [Alternate angles]

In ∆ ACB, m ∠ ABC = 90°

To cover the distance from C to D the car takes 6 seconds

∴ To cover the distance from D to B the car takes 1⁄2 × 6 = 3 seconds

∴ The car takes 3 seconds to reach the foot of the tower from point D.