Class 10 Practice – Level 2 – Set 1 – Some Application of Trigonometry

Total questions: 25

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

45 m

60 m

30 m

40 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: Heights and Distances

None

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

70°

60°

80°

45°

None

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

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

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

$\displaystyle \dfrac{{10}}{3}$

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

None

The base of a cliff is circular. From the extremities of a diameter of the base the angles of elevation of the top of the cliff are 30° and 60°. If the height of the cliff is 500 m, then the diameter of the base of the cliff is:

Topic: Heights and Distances

30°

40°

$\displaystyle \dfrac{{2000}}{{\sqrt{3}}}\text{ }m$

$\displaystyle \dfrac{{400}}{{\sqrt{3}}}\text{ }m$

None

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

z = 16

z = 12

y = 18

m = 20

None

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

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

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 20 m 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. What should be the distance of the bird from the girl (in meters)? [Given √2 =1.41.]

Topic: Properties of Distance

45.3 m

35.2 m

42.3 m

45.8 m

None

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

7.32 m

3.63 m

5.36 m

4.36 m

None

10.

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 Height

70√4

20√3

60√5

40√5

None

11.

The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-stored building are 30° and 45°, respectively. What is the height of the multi-stored building and the distance between the two buildings?

Topic: Angles of Depression

3(3+ √3) m, 2(3+ √3) m

8(3+ √3) m, 6(3+ √3) m

4(3+ √3) m, 4(3+ √3) m

64(3+ √3) m, 2(3+ √3) m

None

12.

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, What is the width of the river?

Topic: Angles of Depression

2(√3 + 1)m

3(√3 + 1)m

6(√3 + 1)m

8(√3 + 1)m

None

13.

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

10 m

20 m

40 m

5 m

None

14.

A tree breaks due to storm and the broken part bends, so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree.

Topic: Properties of Height

8√3 m

3√3 m

6√3 m

4√3 m

None

15.

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

9√3 m

3√3 m

2√3 m

8√9 m

None

16.

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Then the height of the tower is:

Topic: Height Using Angle of Elevation

60√3 m

10√3 m

30√3 m

20√3 m

None

17.

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

20√3 m

90√3 m

60√3 m

40√3 m

None

18.

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.

Topic: Height Using Angle of Elevation

60 (√(3 −3) m

80 (√(3 −2) m

20 (√(3 −1) m

30 (√(3 −1) m m

None

19.

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, the height of the building will be:

Topic: Height Using Angle of Elevation

$\displaystyle \dfrac{{60}}{3}m$

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

$\displaystyle \dfrac{{50}}{3}m$

$\displaystyle \dfrac{{30}}{3}m$

None

20.

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

87.84 m

60.54 m

57.94 m

77.64 m

None

21.

Two man are on opposite sides of a tower. The measure the angle of elevation of the top of tower as 30° and 45° respectively. If the height of the tower is 50 meters, find the distance between the two men.

Topic: Angle of Elevation and Distance

366.6 m

136.6 m

693.6 m

146.6 m

None

22.

An observer 1.5 m tall is 30 m away from a chimney. The angle of elevation of the top of the chimney from his eye is 60°. Find the height of the chimney.

Topic: Height Using Angle of Elevation

93.4 m

53.4 m

43.3 m

63.8 m

None

23.

A tower stands vertically on the ground. From a point on the ground which is 20 m away from the foot of the tower, the angle of elevation of its top is found to be 60°. Find the height of the tower.

Topic: Height Using Angle of Elevation

64.64 m

84.64 m

36.64 m

34.64 m

None

24.

On a horizontal plane, there is a vertical tower with a flagpole on the top of the tower. At a point 9 meters away from the foot of the tower the angle of elevation of the top and bottom of the flagpole are 60 o and 30 o respectively. Find the height of the tower and the flagpole mounted on it respectively.

Topic: Height Using Angle of Elevation

9√3 m, 6√3 m

6√3 m, 12√3 m

3√3 m, 6√3 m

4√3 m, 6√3 m

None

25.

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

50 m

60 m

10 m

30 m

None

1 out of 25

Time's up

Class 10 Practice – Level 2 – Set 1 – Some Application of Trigonometry

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