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SparkEd Math offers 60+ practice questions for Some Applications of Trigonometry across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

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Is SparkEd's Some Applications of Trigonometry content aligned with the CBSE syllabus?

Yes, all Some Applications of Trigonometry questions and lessons on SparkEd Math are fully aligned with the Central Board of Secondary Education (CBSE) syllabus for Class 10. The content follows the official curriculum structure and exam pattern.

Some Applications of Trigonometry — Class 10 CBSE (2025-26)

About Some Applications of Trigonometry — Class 10 CBSE

Solve real-world problems on heights and distances using trigonometric ratios. This topic is part of the CBSE Class 10 mathematics syllabus (chapter: Chapter 9). On this page you can practice 63 questions across three difficulty levels — 20 easy, 22 medium, and 21 hard — each with a visual step-by-step solution, plus a timed 38-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Some Applications of Trigonometry — solved examples for Class 10 CBSE

Example 1easy

Which of the following statements correctly defines the angle of elevation?

A)The angle formed by the line of sight with the vertical line, when the object is above the horizontal level.
B)The angle formed by the line of sight with the horizontal line, when the object is above the horizontal level.
C)The angle formed by the line of sight with the horizontal line, when the object is below the horizontal level.
D)The angle formed between the observer's eye and the top of the object.

Step-by-step solution

The angle of elevation is defined as the angle formed by the line of sight with the horizontal line when the observer looks upwards at an object.
This means the object is above the horizontal level of the observer's eye.

Answer: The angle formed by the line of sight with the horizontal line, when the object is above the horizontal level.

Example 2medium

A pole 15 m high breaks due to a storm and its broken part bends so that the top of the pole touches the ground making an angle of 30° with the ground. At what height from the base did the pole break?

A)5 m
B)7.5 m
C)10 m
D)12.5 m

Step-by-step solution

Let the total height of the pole be H = 15 m. Let the pole break at a height 'x' from the ground. So, the unbroken part is 'x'.
The broken part will be (15 - x) m. This broken part acts as the hypotenuse of the right-angled triangle formed with the ground.
In the right-angled triangle, the height 'x' is opposite to the 30° angle, and the broken part (15 - x) is the hypotenuse. We use the sine ratio: sin(30°) = Opposite/Hypotenuse = x / (15 - x).
We know sin(30°) = 1/2. So, 1/2 = x / (15 - x). Cross-multiply: 15 - x = 2x. This gives 15 = 3x, so x = 5 m.

Answer: 5 m

Example 3hard

A man on top of a 75 m high tower observes two cars on opposite sides of the tower. The angles of depression of the cars are 30° and 45° respectively. Assuming the cars and the base of the tower are in a straight line, what is the distance between the two cars? (Take √3 = 1.732)

A)75(1 + √3) m
B)75√3 m
C)75(√3 - 1) m
D)150 m

Step-by-step solution

Let the height of the tower be H = 75 m. Let the positions of the cars be A and B, and the base of the tower be C. Let the top of the tower be D.
For car A, angle of depression is 30°. In ΔADC, tan 30° = CD/AC => 1/√3 = 75/AC => AC = 75√3 m.
For car B, angle of depression is 45°. In ΔBDC, tan 45° = CD/BC => 1 = 75/BC => BC = 75 m.
The distance between the two cars is AB = AC + BC = 75√3 + 75 = 75(√3 + 1) m.

Answer: 75(1 + √3) m

Practice questions on Some Applications of Trigonometry

Q1.easy
A person standing on a 50 m high cliff observes a boat in the sea. The angle of depression of the boat is formed by the line of sight and:
1. A)the vertical line from the observer's eye to the sea.
2. B)the horizontal line above the line of sight.
3. C)the line connecting the base of the cliff to the boat.
4. D)the horizontal line at the level of the sea.
Show answer
Answer: the horizontal line above the line of sight.
Hint: Just like the angle of elevation, the angle of depression is also measured from a horizontal line. Consider where the observer's horizontal line would be.
Q2.easy
A boy is standing on the ground and looking at the top of a 10-meter tall tree. His eye level is 1.5 m above the ground. If the angle of elevation of the top of the tree from his eye is 45°, what is the horizontal distance between the boy and the tree?
1. A)10 m
2. B)8.5 m
3. C)11.5 m
4. D)1.5 m
Show answer
Answer: 8.5 m
Hint: Remember that the angle of elevation is measured from the eye level of the observer. Adjust the height of the tree accordingly for the right-angled triangle.
Q3.easy
Ravi is trying to find the height of a building. He is standing at a point A on the ground and observes the top of a building at point B. He incorrectly draws the angle of depression from B to A as the angle between the line BA and the vertical line passing through B. What is the correct way to represent the angle of depression from B to A (assuming A is on the ground, B is the top of the building)?
1. A)The angle between the line BA and the line segment AC, where C is the foot of the building.
2. B)The angle between the horizontal line through B and the line of sight BA.
3. C)The angle between the line BA and the line segment BC, where C is the foot of the building.
4. D)The angle at point A formed by the line BA and the horizontal ground.
Show answer
Answer: The angle between the horizontal line through B and the line of sight BA.
Hint: The angle of depression is always measured from a horizontal line at the observer's position, looking down towards the object.
Q4.medium
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°. Assuming that there is no slack in the string, find the length of the string.
1. A)40√3 m
2. B)60√3 m
3. C)80√3 m
4. D)120/√3 m
Show answer
Answer: 40√3 m
Hint: Draw a right-angled triangle. The height of the kite is the perpendicular, and the string length is the hypotenuse. Which trigonometric ratio connects these?
Q5.medium
Which of the following statements is TRUE regarding angles of elevation and depression?
1. A)The angle of elevation is always greater than the angle of depression for the same object and observer.
2. B)The angle of depression is formed when the observer looks upwards from a horizontal line.
3. C)If an observer at point A looks at an object at point B, the angle of elevation from A to B is equal to the angle of depression from B to A.
4. D)The line of sight is always horizontal for both angle of elevation and depression.
Show answer
Answer: If an observer at point A looks at an object at point B, the angle of elevation from A to B is equal to the angle of depression from B to A.
Hint: Recall the definitions of angle of elevation and depression, and how they relate to parallel horizontal lines and the line of sight.
Q6.medium
From a point on the ground, 30 m away from the foot of a tower, the angle of elevation of the top of the tower is 30°. The angle of elevation of the top of a water tank on the top of the tower is 45°. Find the height of the water tank.
1. A)(30√3 - 30) m
2. B)30(√3 - 1) m
3. C)30(1 - 1/√3) m
4. D)30(√3 + 1) m
Show answer
Answer: 30(1 - 1/√3) m
Hint: Consider two right-angled triangles. One formed by the tower, and another by the tower + water tank. Both share the same base distance.
Q7.hard
A car is moving towards a tower. It takes 12 minutes for the angle of depression from the top of the tower to the car to change from 30° to 60°. How much more time will the car take to reach the base of the tower from the point where the angle of depression is 60°?
1. A)4 minutes
2. B)6 minutes
3. C)8 minutes
4. D)10 minutes
Show answer
Answer: 6 minutes
Hint: Assume the height of the tower is 'h' and the speed of the car is 'v'. Use trigonometric ratios to express distances in terms of 'h' and angles, then relate distance and time.
Q8.hard
From two points P and Q at distances 'a' and 'b' respectively (where a > b) from the base of a tower and in the same straight line with it, the angles of elevation of the top of the tower are complementary. Which of the following expressions correctly represents the height of the tower?
1. A)√(a + b)
2. B)√(ab)
3. C)a + b
4. D)ab
Show answer
Answer: √(ab)
Hint: Let the height of the tower be 'h'. If one angle is θ, the complementary angle is (90° - θ). Use the tangent ratio for both angles.
Q9.hard
The angle of elevation of the top of a building from the foot of a 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 60 m high, what is the height of the building?
1. A)10 m
2. B)15 m
3. C)20 m
4. D)30 m
Show answer
Answer: 20 m
Hint: Draw two separate right-angled triangles sharing a common base. Use the known height of the tower and its angle of elevation to find the common base first.

These are 9 of the 63 questions available for Some Applications of Trigonometry. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.