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Class 10 Quiz Level 2 (Moderate) – Some Application of Trigonometry

Total questions: 20

1.

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: Heights and Distances

Deselect Answer

45 m

60 m

30 m

40 m

None

2.

If a flagstaff of 6 m height placed on the top of a tower throws a shadow of 2 √3 m along the ground, then the angle (in degrees) that the sun makes with the ground is:

Topic: Angle of Elevation

Deselect Answer

70°

60°

80°

45°

None

3.

A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?

Topic: Properties of Length

Deselect Answer

9√3 m

3√3 m

2√3 m

8√9 m

None

4.

The angles of elevation of the top of a tower from two points at distances of 5 metres and 20 metres from the base of the tower and in the same straight line with it, are complimentary. Find the height of the tower.

Topic: Complementary Angles of Elevation

Deselect Answer

50 m

60 m

10 m

30 m

None

5.

A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. What is the length of the staring, assume that there is no slack in the string?

Topic: Properties of Length

Deselect Answer

20√3 m

90√3 m

60√3 m

40√3 m

None

6.

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 of P is equal to (in m):

Topic: Properties of Height

Deselect Answer

z = 16

z = 12

y = 18

m = 20

None

7.

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. (Take√3=1.732 )

Topic: Properties of Height

Deselect Answer

7.32 m

3.63 m

5.36 m

4.36 m

None

8.

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°.

Topic: Properties of Height

Deselect Answer

10 m

20 m

40 m

5 m

None

9.

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 30 meters away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and width of the river (in meter). [Take √3 =1.732.]

Topic: Heights and Distances

Deselect Answer

h = 36.98, width = 36 m

h = 26.88, width = 19 m

h = 55.98, width = 16 m

h = 25.98, width = 15 m

None

10.

The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45° . If the angle of elevation of the top of a flags tagg fixed at the top of the tower, at A is 60°, then find the height of the flagstaff. [Use √3=1.732]

Topic: Height using Trigonometry

Deselect Answer

87.84 m

60.54 m

57.94 m

77.64 m

None

11.

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6 m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 60°. Find the height of the tower. [Use √3=1.732]

Topic: Properties of Height

Deselect Answer

3 m

4 m

10 m

60 m

None

12.

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 30 meters away from the bank, he finds the angle of elevation to be 30° . Find the width of the river.(in meters) [Take √3 =1.732.]

Topic: Angle of Elevation

Deselect Answer

30 m

60 m

15 m

20 m

None

13.

From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of the tower is 60°. The angle of elevation of the top of a water tank (on the top of the tower) is 45°. Find the height of the tower.

Topic: Height Using Angle of Elevation

Deselect Answer

23.1 m

36.2 m

53.3 m

56.1 m

None

14.

Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point P between them on the road, the angle of elevation of the top of one pole is 60° and the angle of depression from the top of another pole at P is 30°. Find the height of each pole.

Topic: Angles of Elevation and Depression

Deselect Answer

20√3 m

40√3 m

60√3 m

50√3 m

None

15.

From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pole are 30° and 45° respectively. Find the height of the pole.

Topic: Height using Angles of Depression

Deselect Answer

41.13 m

36.13 m

22.13 m

21.13 m

None

16.

Find the angle of elevation of the sun when the shadow of a pole h meters high is √3h meters long.

Topic: Angle of Elevation

Deselect Answer

40°

60

30°

15°

None

17.

An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower the eye of the observer.

Topic: Angle of Elevation

Deselect Answer

90°

45°

30°

60°

None

18.

Amit, standing on a horizontal plane, finds a bird flying at a distance of 200 m from him at an elevation of 30°. Deepak standing on the roof of a 50 m high building, finds the angle of elevation of the same bird to be 45°. Amit and Deepak are on opposite sides of the bird. Find the distance of the bird from Deepak.

Topic: Properties of Distance

Deselect Answer

50√3 m

80√2 m

50√2 m

61√2 m

None

19.

The ratio of the length of a rod and its shadow is 1: $\displaystyle \dfrac{1}{{\sqrt{3}}}$ . What is the angle of elevation of the source of light?

Topic: Angle of Elevation

Deselect Answer

30°

60°

35°

40°

None

20.

An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney?

Deselect Answer

60 m

90 m

50 m

30 m

None

1 out of 20

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