Grade 10 Math Quiz: Applications of Trigonometry | Concept of Maths

Question 1

1. If the length of the shadow of a vertical pole on the horizontal ground is equal to its height, then what is the angle of elevation of the sun?

A) \( 30^\circ \)

B) \( 45^\circ \)

C) \( 60^\circ \)

D) \( 90^\circ \)

Answer

Correct Answer: B

Question 2

2. A ladder leaning against a wall makes an angle of \( 60^\circ \) with the horizontal ground. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder.

A) \( 5 \text{ m} \)

B) \( 2.5 \text{ m} \)

C) \( 5\sqrt{3} \text{ m} \)

D) \( \frac{5}{\sqrt{3}} \text{ m} \)

Answer

Correct Answer: A

Question 3

3. The height of a tower is 10 m. What is the length of its shadow when the Sun's altitude is \( 30^\circ \)?

A) \( \frac{10}{\sqrt{3}} \text{ m} \)

B) \( 10\sqrt{3} \text{ m} \)

C) \( 10 \text{ m} \)

D) \( 5\sqrt{3} \text{ m} \)

Answer

Correct Answer: B

Question 4

4. 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, making an angle of \( 60^\circ \) with the ground. Assuming there is no slack, what is the length of the string?

Question 5

5. 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 \( 30^\circ \). The height of the tower is:

A) \( 30\sqrt{3} \text{ m} \)

B) \( 15\sqrt{3} \text{ m} \)

C) \( 10\sqrt{3} \text{ m} \)

D) \( 10 \text{ m} \)

Answer

Correct Answer: C

Question 6

6. 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 \( 45^\circ \). What is the height of the chimney?

A) \( 27 \text{ m} \)

B) \( 28.5 \text{ m} \)

C) \( 30 \text{ m} \)

D) \( 31.5 \text{ m} \)

Answer

Correct Answer: C

Question 7

7. 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 \( 60^\circ \) and \( 30^\circ \). The height of the poles is:

A) \( 10\sqrt{3} \text{ m} \)

B) \( 20\sqrt{3} \text{ m} \)

C) \( 40\sqrt{3} \text{ m} \)

D) \( 20 \text{ m} \)

Answer

Correct Answer: B

Question 8

8. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is \( 60^\circ \) and the angle of depression of its foot is \( 45^\circ \). Determine the height of the tower.

A) \( 7(\sqrt{3} - 1) \text{ m} \)

B) \( 7\sqrt{3} \text{ m} \)

C) \( 14 \text{ m} \)

D) \( 7(\sqrt{3} + 1) \text{ m} \)

Answer

Correct Answer: D

Question 9

9. A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground, making an angle of \( 30^\circ \) with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the original total height of the tree.

A) \( 8\sqrt{3} \text{ m} \)

B) \( 24\sqrt{3} \text{ m} \)

C) \( \frac{8}{\sqrt{3}} \text{ m} \)

D) \( 16\sqrt{3} \text{ m} \)

Answer

Correct Answer: A

Question 10

10. The angles of elevation of the top of a tower from two points at a distance of \( a \) and \( b \) from the base and in the same straight line with it are complementary. What is the height of the tower?

A) \( a + b \)

B) \( \sqrt{ab} \)

C) \( \frac{a+b}{2} \)

D) \( ab \)

Answer

Correct Answer: B

Question 11

11. The angle of depression of a car standing on the ground, from the top of a 15 m high tower, is \( 30^\circ \). The distance of the car from the base of the tower is:

A) \( 15\sqrt{3} \text{ m} \)

B) \( 5\sqrt{3} \text{ m} \)

C) \( 15 \text{ m} \)

D) \( 30 \text{ m} \)

Answer

Correct Answer: A

Question 12

12. An observer on top of a 100 m tall lighthouse sees two ships on the same side of the lighthouse. The angles of depression of the two ships are \( 45^\circ \) and \( 30^\circ \). What is the distance between the two ships?

A) \( 100(\sqrt{3} + 1) \text{ m} \)

B) \( 100(\sqrt{3} - 1) \text{ m} \)

C) \( 100 \text{ m} \)

D) \( 50\sqrt{3} \text{ m} \)

Answer

Correct Answer: B

Question 13

13. The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude drops from \( 60^\circ \) to \( 30^\circ \). The height of the tower is:

A) \( 40\sqrt{3} \text{ m} \)

B) \( 20\sqrt{3} \text{ m} \)

C) \( 20 \text{ m} \)

D) \( 60 \text{ m} \)

Answer

Correct Answer: B

Question 14

14. If the ratio of the length of a vertical rod and the length of its shadow is \( 1:\sqrt{3} \), then the angle of elevation of the sun is:

A) \( 30^\circ \)

B) \( 45^\circ \)

C) \( 60^\circ \)

D) \( 90^\circ \)

Answer

Correct Answer: A

Question 15

15. An aeroplane is flying horizontally at a height of 3000 m. It passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are \( 60^\circ \) and \( 45^\circ \) respectively. The vertical distance between the aeroplanes at that instant is:

A) \( 1000(3 - \sqrt{3}) \text{ m} \)

B) \( 1000(\sqrt{3} - 1) \text{ m} \)

C) \( 3000(3 - \sqrt{3}) \text{ m} \)

D) \( 1000\sqrt{3} \text{ m} \)

Answer

Correct Answer: A

Question 16

16. A man on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 6 seconds for the angle of depression to change from \( 30^\circ \) to \( 60^\circ \), how soon after this will the car reach the foot of the tower?

A) 2 seconds

B) 3 seconds

C) 4 seconds

D) 6 seconds

Answer

Correct Answer: B

Question 17

17. The angle of elevation of a stationary cloud from a point \( h \) meters above a lake is \( \alpha \) and the angle of depression of its reflection in the lake is \( \beta \). The height of the cloud above the lake surface is:

A) \( h \left( \frac{\tan \beta - \tan \alpha}{\tan \beta + \tan \alpha} \right) \)

B) \( h \left( \frac{\tan \alpha + \tan \beta}{\tan \alpha - \tan \beta} \right) \)

C) \( h \left( \frac{\tan \beta + \tan \alpha}{\tan \beta - \tan \alpha} \right) \)

D) \( h \left( \frac{\tan \alpha - \tan \beta}{\tan \alpha + \tan \beta} \right) \)

Answer

Correct Answer: C

Question 18

18. The tops of two poles of heights 16 m and 10 m are connected by a taut wire. If the wire makes an angle of \( 30^\circ \) with the horizontal, find the length of the wire.

A) \( 10 \text{ m} \)

B) \( 12 \text{ m} \)

C) \( 14 \text{ m} \)

D) \( 16 \text{ m} \)

Answer

Correct Answer: B

Question 19

19. A weather balloon is connected to a meteorological station by a cable of length 215 m inclined at \( 60^\circ \) to the ground. Determine the height of the balloon from the ground. (Assume the cable has no slack)

A) \( 107.5 \text{ m} \)

B) \( 215\sqrt{3} \text{ m} \)

C) \( 107.5\sqrt{3} \text{ m} \)

D) \( \frac{215}{\sqrt{3}} \text{ m} \)

Answer

Correct Answer: C

Question 20

20. From a point 20 m away from the base of a tower, the angle of elevation to the top of the tower is \( 45^\circ \). What is the height of the tower?

A) \( 10 \text{ m} \)

B) \( 20\sqrt{3} \text{ m} \)

C) \( \frac{20}{\sqrt{3}} \text{ m} \)

D) \( 20 \text{ m} \)

Answer

Correct Answer: D

Accepted Answer

Correct Answer: A

Master Trig Applications: Grade 10 Math Quiz | Concept of Maths

Master Trig Applications: Grade 10 Math Quiz | Concept of Maths

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5. 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 \( 30^\circ \). The height of the tower is:

6. 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 \( 45^\circ \). What is the height of the chimney?

7. 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 \( 60^\circ \) and \( 30^\circ \). The height of the poles is:

8. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is \( 60^\circ \) and the angle of depression of its foot is \( 45^\circ \). Determine the height of the tower.

9. A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground, making an angle of \( 30^\circ \) with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the original total height of the tree.

10. The angles of elevation of the top of a tower from two points at a distance of \( a \) and \( b \) from the base and in the same straight line with it are complementary. What is the height of the tower?

11. The angle of depression of a car standing on the ground, from the top of a 15 m high tower, is \( 30^\circ \). The distance of the car from the base of the tower is:

12. An observer on top of a 100 m tall lighthouse sees two ships on the same side of the lighthouse. The angles of depression of the two ships are \( 45^\circ \) and \( 30^\circ \). What is the distance between the two ships?

13. The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude drops from \( 60^\circ \) to \( 30^\circ \). The height of the tower is:

14. If the ratio of the length of a vertical rod and the length of its shadow is \( 1:\sqrt{3} \), then the angle of elevation of the sun is:

16. A man on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 6 seconds for the angle of depression to change from \( 30^\circ \) to \( 60^\circ \), how soon after this will the car reach the foot of the tower?

17. The angle of elevation of a stationary cloud from a point \( h \) meters above a lake is \( \alpha \) and the angle of depression of its reflection in the lake is \( \beta \). The height of the cloud above the lake surface is:

18. The tops of two poles of heights 16 m and 10 m are connected by a taut wire. If the wire makes an angle of \( 30^\circ \) with the horizontal, find the length of the wire.

19. A weather balloon is connected to a meteorological station by a cable of length 215 m inclined at \( 60^\circ \) to the ground. Determine the height of the balloon from the ground. (Assume the cable has no slack)

20. From a point 20 m away from the base of a tower, the angle of elevation to the top of the tower is \( 45^\circ \). What is the height of the tower?

Grade 10 Math Quiz: Applications of Trigonometry | Concept of Maths

1. If the length of the shadow of a vertical pole on the horizontal ground is equal to its height, then what is the angle of elevation of the sun?

2. A ladder leaning against a wall makes an angle of \( 60^\circ \) with the horizontal ground. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder.

3. The height of a tower is 10 m. What is the length of its shadow when the Sun's altitude is \( 30^\circ \)?

4. 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, making an angle of \( 60^\circ \) with the ground. Assuming there is no slack, what is the length of the string?

Master Trig Applications: Grade 10 Math Quiz | Concept of Maths

Master Trig Applications: Grade 10 Math Quiz | Concept of Maths

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5. 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 \( 30^\circ \). The height of the tower is:

6. 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 \( 45^\circ \). What is the height of the chimney?

7. 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 \( 60^\circ \) and \( 30^\circ \). The height of the poles is:

8. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is \( 60^\circ \) and the angle of depression of its foot is \( 45^\circ \). Determine the height of the tower.

9. A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground, making an angle of \( 30^\circ \) with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the original total height of the tree.

10. The angles of elevation of the top of a tower from two points at a distance of \( a \) and \( b \) from the base and in the same straight line with it are complementary. What is the height of the tower?

11. The angle of depression of a car standing on the ground, from the top of a 15 m high tower, is \( 30^\circ \). The distance of the car from the base of the tower is:

12. An observer on top of a 100 m tall lighthouse sees two ships on the same side of the lighthouse. The angles of depression of the two ships are \( 45^\circ \) and \( 30^\circ \). What is the distance between the two ships?

13. The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude drops from \( 60^\circ \) to \( 30^\circ \). The height of the tower is:

14. If the ratio of the length of a vertical rod and the length of its shadow is \( 1:\sqrt{3} \), then the angle of elevation of the sun is:

16. A man on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 6 seconds for the angle of depression to change from \( 30^\circ \) to \( 60^\circ \), how soon after this will the car reach the foot of the tower?

17. The angle of elevation of a stationary cloud from a point \( h \) meters above a lake is \( \alpha \) and the angle of depression of its reflection in the lake is \( \beta \). The height of the cloud above the lake surface is:

18. The tops of two poles of heights 16 m and 10 m are connected by a taut wire. If the wire makes an angle of \( 30^\circ \) with the horizontal, find the length of the wire.

19. A weather balloon is connected to a meteorological station by a cable of length 215 m inclined at \( 60^\circ \) to the ground. Determine the height of the balloon from the ground. (Assume the cable has no slack)

20. From a point 20 m away from the base of a tower, the angle of elevation to the top of the tower is \( 45^\circ \). What is the height of the tower?