CBSE Class 10-Mathematics: Chapter –9 Some Applications of Trigonometry Part 19

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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.

Right Triangle ABP

Right Triangle ABP

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Answer:

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 .

The angles of elevation of the top of a tower

The Angles of Elevation of the Top of a Tower

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Answer:

Let

Then,

In right triangle ABP,

In right triangle ABQ,

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

Hence, the height of the tower is .

Proved