# Important Questions for CBSE Class 10 Maths Chapter 9 - Some Applications of Trigonometry 4 Mark Question

## CBSE Class 10 Maths Chapter-9 Some Applications of Trigonometry – Free PDF Download

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CBSE Class 10 Maths Chapter-9 Some Applications of Trigonometry Important Questions

## 4 Mark Questions

1. The angle of elevation of the top of a building from the foot of the tower is  and the angle of elevation of the top of the tower from the foot of the building is If the tower is 50 m high, find the height of the building.

Ans . Let the height of the building be  m.

BQ =  m ……….(i)
In right triangle ABQ,

BQ =  m ……….(ii)
From eq. (i) and (ii),

m

2. Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are  and  respectively. Find the height of the poles and the distances of the point from the poles.

Ans. In right triangle ABC,

AB =  m ……….(i)
In right triangle ABD,

AB =  m ……….(ii)
From eq. (i) and (ii),
=
3BC = BC + 20
BC = 10 m
From eq. (i), AB =  m
Hence height of the tower is  m and the width of the canal is 10 m.

3. A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any distant is  After some time, the angle of elevation reduces to  (see figure). Find the distance travelled by the balloon during the interval.

Ans. In right triangle ABC,

BC =  m
In right triangle PQC,

= 176.4
BQ =  =
=  =  m
Hence the distance travelled by the balloon during the interval is  m.

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.

Ans. In right triangle ABP,

BP = AB ……….(i)
In right triangle ABQ,

BQ =  ……….(ii)
PQ = BP – BQ
PQ = AB =  = 2BQ [From eq. (ii)]
BQ =  PQ
Time taken by the car to travel a distance PQ = 6 seconds.
Time taken by the car to travel a distance BQ, i.e.  PQ =  x 6 = 3 seconds.
Hence, the further time taken by the car to reach the foot of the tower is 3 seconds.

5. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

Ans. Let APB =
Then, AQB =
[APB and AQB are complementary]
In right triangle ABP,

……….(i)
In right triangle ABQ,
=
……….(ii)
Multiplying eq. (i) and eq. (ii),

AB2 = 36
AB = 6 m
Hence, the height of the tower is 6 m.
Proved.