# CBSE Class 10-Mathematics: Chapter – 9 Some Applications of Trigonometry Part 19 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 4:

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 , 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 . Find the time taken by the car to reach the foot of the tower from this point.

In right triangle ABP,

In right triangle ABQ,

Time taken by the car to travel a distance BQ,

i.e.. seconds.

Hence, the further time taken by the car to reach the foot of the tower is seconds.

Question 5:

The angles of elevation of the top of a tower from two points at a distance of and from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is .

Let

Then,

In right triangle ABP,

In right triangle ABQ,

Multiplying eq. (i) and eq. (ii) ,

Hence, the height of the tower is .

Proved