Class 10 Practice – Level 3 – Set 1 – Some Application of Trigonometry

Total questions: 15

A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal.

Topic: Angles of Elevation and Depression

15√3 m, 20 m

10√3m, 10 m

80√3 m, 40 m

20√3 m, 20 m

None

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Find the height of the tower.

Topic: Angles of Elevation and Depression

7(√3+1) m

9(√3+1) m

8(√3+1) m

4(√3+1) m

None

As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Topic: Angles of Depression

120 m

100 m

150 m

160 m

None

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 instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance (in m) travelled by the balloon during the interval.

Topic: Angle of Elevation and Distance

51√3

56√3

68√3

58√3

None

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.

Topic: Relative Motion and Angle of Depression

12 sec

6 sec

3 sec

10 sec

None

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. Find the height of the tower.

Topic: Complementary Angles and Height

6 m

7 m

10 m

12 m

None

From a balloon vertically above a straight road, the angles of depression of two cars at an instant are found to be 45° and 60°. If the cars are 100 m apart, find the height of the balloon.

Topic: Height using Angles of Depression

90(3+√3) m

80(3+√3) m

60(3+√3) m

50(3+√3) m

None

Two vertical poles of equal heights are 120 m apart. On the line joining their bottoms, A and B are two points. Angle of elevation of the top of one pole from A is 45 ∘ and that of the other pole from B is also 45°. If AB=30 m, then the height of each pole is:

Topic: Angle of Elevation and Distance

90 m

60 m

40 m

45 m

None

If PQ is a vertical tower subtending angles α,β, γ at the points A,B,C, respectively, on the line in the horizontal plane through the foot Q of tower and on the same side of it, then BC cotα−CA cotβ + ABcotγ is equal to

Topic: Angles of Elevation and Depression

None

10.

Some portion of a 20 m long tree is broken by the wind and the top struck the ground at an angle of 30°. The height of the point where the tree is broken is:

Topic: Properties of Height

$\displaystyle \dfrac{{25}}{3}$ m

$\displaystyle \dfrac{{6}}{3}$ m

$\displaystyle \dfrac{{20}}{3}$ m

$\displaystyle \dfrac{{80}}{3}$ m

None

11.

Two vertical poles AL and BM of heights 20 m and 80 m, respectively, stand apart on a horizontal plane. If A, B are the feet of the poles and AM and BL intersect at P, then the height (in m) of P is equal to:

Topic: Properties of Height

z = 66

z = 16

z = 33

z = 22

None

12.

A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30° . A girl standing on the roof of a 20m high building, finds the angle of elevation of the same bird to be 45° . The boy and the girl are on the opposite sides of the bird. Find the distance of the bird from the girl (in meters). [Given √2 =1.41.]

Topic: Angle of Elevation

42.3 m

35.2 m

45.8 m

45.3 m

None

13.

From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff and the distance of the building from the point P. (You may take√3=1.732 )

Topic: Properties of Length

3.63 m

5.36 m

7.32 m

4.36 m

None

14.

The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30° than when it is 60°. Find the height of the tower.

Topic: Properties of Length

70√4 m

60√5 m

40√5 m

20√3 m

None

15.

From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°, respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.

Topic: Angles of Depression and Width

6(√3 + 1)m

8(√3 + 1)m

3(√3 + 1)m

2(√3 + 1)m

None

1 out of 15

Time's up

Class 10 Practice – Level 3 – Set 1 – Some Application of Trigonometry

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