Class 10 Quiz Level 1 (Easy) – Some Application of Trigonometry

Total questions: 30

From the hay loft door, Sid sees his dog on the ground. The angle of depression of the dog is 40º. Sid's eye level is 16 feet above the ground. How many feet must the dog walk to reach the open barn door directly below Sid?

Topic: Angle of Depression And Distance

Deselect Answer

25 ft

19 ft

38 ft

50 ft

None

A shopper is standing on level ground 800 feet from the base of a 250 foot tall department store. The shopper looks up and sees a flag on the store's roof. To the nearest degree what is the angle of elevation to the top of the building from the point on the ground where the shopper is standing?

Topic: Angle of Elevation

Deselect Answer

17°

23°

45°

33°

None

A flag pole 18 feet tall casts a shadow 12 feet long at a specific time of day. Find the angle of elevation of the sun at this time of day.

Topic: Angle of Elevation

Deselect Answer

54º

46º

56º

65º

None

From the top of a tower of height 50 m, find the angles of depression of the top and bottom of a pole are 30° and 45° respectively. Find the height of the pole. (Use √3=1⋅732 )

Topic: Angles of Depression

Deselect Answer

41.13 m

21.13 m

36.13 m

22.13 m

None

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?

Topic: Height Using Angle of Elevation

Deselect Answer

40 m

60 m

50 cm

30 m

None

From the top of a cliff 20 m high, the angle of elevation of the top of a tower is found to be equal to the angle of depression of the foot of the tower. Then, find height of the tower.

Topic: Height Using Angle of Elevation

Deselect Answer

20 m

60 m

40 m

80 m

None

A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower.

Topic: Angle of Elevation

Deselect Answer

35√4 m

65√8 m

15√3 m

18√3 m

None

In the given figure, the angles of depressions from the observing positions $\displaystyle {{O}_{1}}$ and $\displaystyle {{O}_{2}}$ respectively of the object at A are:

Topic: Angles of Depression

Deselect Answer

30°, 45°

60°, 45°

30°, 60°

60°, 30°

None

From a point on the ground 47 feet from the foot of a tree, the angle of elevation of the top of the tree is 35º. Find the height of the tree.

Topic: Angle of Elevation

Deselect Answer

42.06 ft

32.90 ft

50.90 ft

43.50 ft

None

10.

A vertical pole stands on the level ground. From a point on the ground, 25 m away from the foot of the pole, the angle of elevation of its top is found to be 60°. Find the height of the pole. [Take √3=1.732.]

Topic: Angle of Elevation

Deselect Answer

32.3 m

56.2 m

43.3 m

56.3 m

None

11.

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: Rope and Angle with Ground

Deselect Answer

15 m

20 m

25 m

10 m

None

12.

An observer, 1.7 m tall, is 20√3 m away from a tower. The angle of elevation from the eye of observer to the top of tower is 30°. Find the height of tower.

Topic: Angle of Elevation

Deselect Answer

21.8 m

31.7 m

41.9 m

21.7 m

None

13.

The height of a tower is 10 m. Calculate the length of its shadow, when the sun's altitude is 45°.

Topic: Properties of Length

Deselect Answer

10 m

12 m

15 m

18 m

None

14.

A 8 foot metal guy wire is attached to a broken stop sign to secure its position until repairs can be made. Attached to a stake in the ground, the guy wire makes an angle of 51º with the ground. How far from the foot of the stop sign is the stake?

Topic: Properties of Distance

Deselect Answer

5.03 ft

4.25 ft

6.71 ft

7.80 ft

None

15.

A ladder 15 m long makes an angle of 60° with the wall. Find the height of the point where the ladder touches the wall.

Topic: Properties of Height

Deselect Answer

7.5 m

6.5 m

8.5 m

9.5 m

None

16.

On a windy day, a 90 foot rope tightly secures a hot air balloon to a stake in the ground. From the balloon, the angle of depression of the stake is 62º. Find the height of the balloon, assuming the wind to be constant.

Topic: Properties of Height

Deselect Answer

85.8 ft

68.6 ft

79.5 ft

97.5 ft

None

17.

A pole casts a shadow of length 2√3 m on the ground, when the sun's elevation is 60°. Find the height of the pole.

Topic: Height Using Angle of Elevation

Deselect Answer

6 m

10 m

15 m

4 m

None

18.

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. Given that √3 =1.732.

Topic: Height Using Angle of Elevation

Deselect Answer

19.124 m

19.457 m

14.124 m

56.234 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

60°

30°

40°

35°

None

20.

A man in a boat rowing away from a light house 100 m high takes 2 minutes to change the angle of elevation of the top of the light house from 60° to 30°. Find the speed of the boat in metres per minute. [ Use √3=1.732]

Topic: Angle of Elevation

Deselect Answer

57.73 m/min.

67.00 m/min.

26.53 m/min.

89.73 m/min.

None

21.

A kite is flying at a height of 75 m from the level ground, attached to a string inclined at 60° to the horizontal. Find the length of the string, assuming that there is no slack in it. (in metres)[Take√3 =1.732.]

Topic: Properties of Length

Deselect Answer

50√3 m

30√3 m

80√3 m

60√3 m

None

22.

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?

Topic: Angle of Elevation

Deselect Answer

30 m

50 m

60 m

80 m

None

23.

A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 5 m. From a point on the ground the angles of elevation of the top and bottom of the flagstaff are 60 ∘ and 30 ∘ respectively. Find the height of the tower and the distance of the point from the tower. (Use √3 =1.732)

Topic: Angle of Elevation

Deselect Answer

6.32 m

45.6 m

78.3 m

4.33 m

None

24.

The rod AC of a TV disc antenna is fixed at right angles to the wall AB and a rod CD is supporting the disc as shown in Fig. If AC=1.5 m long and CD=3 m, find (i) tanθ (ii) secθ+cosecθ

Topic: Trigonometric ratios in a right-angled

Deselect Answer

$\displaystyle \dfrac{1}{√3}$, $\displaystyle \dfrac{2}{√3}$ + 2

$\displaystyle \dfrac{2}{√3}$ , $\displaystyle \dfrac{5}{√3}$ + 8,

$\displaystyle \dfrac{1}{√3}$ , $\displaystyle \dfrac{6}{√3}$ + 9

$\displaystyle \dfrac{2}{√3}$ , $\displaystyle \dfrac{2}{√3}$ +5

None

25.

If a tower 30 m high, casts a shadow 10√3 m long on the ground, then what is the angle of elevation of the sun?

Topic: Angle of Elevation

Deselect Answer

80°

60°

120°

40°

None

26.

The shadow of a tower at a time is three times as long as its shadow when the angle of elevation of the sun is 60°. Find the angle of elevation of the sun at the time of the longer shadow.

Topic: Angle of Elevation

Deselect Answer

35°

65°

30°

60°

None

27.

As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are 30º and 45º. If one ship is exactly behind the other on the same side of the light house, the distance between the two ships. [Use √3 = 1.732]

Topic: Properties of Distance

Deselect Answer

73.2 m

63.2 m

36.2 m

43.2 m

None

28.

From the top of a 108 foot lighthouse, the angle of depression of a boat at sea is 27º. Find the horizontal distance from the boat to the base of the lighthouse.

Topic: Angle of Depression And Distance

Deselect Answer

239.05 ft

212.18 ft

204.22 ft

265.15 ft

None

29.

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 was 60°. Find the height of the tower. (Given√3=1.732 )

Topic: Properties of Height

Deselect Answer

78.64 m

65.64 m

45.64 m

34.64 m

None

30.

The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.

Topic: Angle of Depression And Distance

Deselect Answer

95 m

85 m

65 m

36 m

None

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Class 10 Quiz Level 1 (Easy) – Some Application of Trigonometry

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