10TH CBSE MATHS QUIZ applications of trigonometry 100 MCQS

Class 10 Mathematics — Applications of Trigonometry

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Test 1

Applications of Trigonometry

10 Questions

Q1. The angle of depression of a car from the top of a 75 m high tower is 30°. The distance of the car from the base is:

A. 25√3 mB. 50√3 mC. 75√3 mD. 150 m

Q2. The angle of depression of a car from the top of a 150 m high tower is 30°. The horizontal distance of the car from the tower is:

A. 50√3 mB. 150√3 mC. 150√2 mD. 75 m

Q3. Angles of elevation of a tower from two points at distances a and b (a>b) on the same straight line are 30° and 60°. The height of the tower is:

A. √(a+b)B. √abC. √(a−b)D. √(a/b)

Useful Resource: Ravi Test Papers

Q4. Two men are on opposite sides of a 100 m tower and observe its top at 30° and 45°. Their distance apart is:

A. 100(√3−1) mB. 100(1−√3) mC. 100(√3+1) mD. 100 m

Q5. If the angles of elevation from points at distances a and b are complementary, the height h of the tower is:

A. abB. √abC. 2√abD. a+b

Q6. Two poles are 20 m and 14 m high. Their tops are connected by a wire making 30° with the horizontal. The wire length is:

A. 12 mB. 10 mC. 8 mD. 6 m

Useful Resource: CBSE Class 10 Maths

Q7. A 12 m tree breaks so that its top touches the ground and the broken part makes 30° with the ground. The tree breaks at a height of:

A. 9 mB. 6 mC. 4 mD. 8 m

Q8. Two men are on opposite sides of a 60 m tower and observe its top at 60° and 45°. Their distance apart is:

A. 20(√3+3) mB. 20(3−√3) mC. 20(√3−3) mD. 20(√3+1) m

Q9. A 14 m ladder rests against a wall with its foot 7 m from the wall. The angle of elevation is:

A. 60°B. 45°C. 30°D. 75°

Useful Resource: CBSE Class 10 Science

Q10. If the ratio of the height of a pole to the length of its shadow is √3:1, the sun's altitude is:

A. 30°B. 45°C. 75°D. 60°

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Test 2

Applications of Trigonometry

10 Questions

Q1. The angle of elevation is the angle formed by the line of sight with the horizontal when the object is:

A. Above the horizontal levelB. Below the horizontal levelC. At the horizontal levelD. None of these

Q2. If the length of the shadow of a tower is √3 times its height, the sun's angle of elevation is:

A. 45°B. 60°C. 75°D. 30°

Q3. If the height of a tower is √3 times the length of its shadow, the sun's angle of elevation is:

A. 15°B. 30°C. 60°D. 45°

Useful Resource: CBSE Class 10 English

Q4. A river is 60 m wide. A tree stands on one bank. From the point exactly opposite its foot on the other bank, the angle of elevation of the top is 30°. The tree's height is:

A. 30√3 mB. 60 mC. 20√3 mD. 60√3 m

Q5. An electric pole is 10√3 m high and its shadow is 10 m. The sun's elevation is:

A. 45°B. 30°C. 60°D. 15°

Q6. A pole casts a shadow of 20/√3 m when the sun's elevation is 60°. Its height is:

A. 2√3 mB. 4√3 mC. 6 mD. 12 m

Useful Resource: CBSE Class 10 Social Science

Q7. A right triangle has hypotenuse 20 cm and an angle of 60°. Its area is:

A. 50√3 cm²B. 100√3 cm²C. 100 cm²D. 50 cm²

Q8. Two poles are a metres apart and one is twice as high as the other. From the midpoint, their angular elevations are complementary. The smaller height is:

A. √2a mB. a/(2√2) mC. a/√2 mD. 2a m

Q9. A ramp has height 1 m and slopes at 30°. Its length is:

A. √3 mB. 3 mC. 2 mD. 2√3 m

Useful Resource: CBSE Class 10 All Subjects

Q10. The line drawn from the eye of an observer to the point viewed is called the:

A. Horizontal lineB. Vertical lineC. None of theseD. Line of sight

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Test 3

Applications of Trigonometry

10 Questions

Q1. A tower casts a 90 m shadow when the sun's altitude is 60°. Its height is:

A. 60 mB. 90√3 mC. 90 mD. 60√3 m

Q2. A kite is 90 m above the ground and its string makes 60° with the horizontal. The string length is:

A. 60√3 mB. 90 mC. 90√3 mD. 45 m

Q3. A rod and its shadow are in the ratio 1:√3. The sun's angle of elevation is:

A. 30°B. 45°C. 60°D. 90°

Useful Resource: Ravi Test Papers .in

Q4. A point on the ground is 30 m from the foot of a tower and the angle of elevation is 30°. The tower height is:

A. 30 mB. 10√3 mC. 30√3 mD. 10 m

Q5. A tower subtends 30° at a point on the same level as its foot. At a second point h metres above the first, the depression of the foot is 60°. If the horizontal distance from the first point to the tower is 30 m, the tower height is:

A. 10 mB. 30 mC. 10√3 mD. 30√3 m

Q6. If the length of a tower's shadow is increasing, the angle of elevation of the sun is:

A. DecreasingB. IncreasingC. ZeroD. Neither increasing nor decreasing

Useful Resource: RAVI MATHS TUITION CENTRE YouTube

Q7. If the height of a tower is √3 times the length of its shadow, the sun's elevation is:

A. 30°B. 60°C. 45°D. 15°

Q8. If the ratio of pole height to shadow is 1:√3, the sun's elevation is:

A. 90°B. 60°C. 30°D. 45°

Q9. Two towers of heights x and y stand on level ground. From the midpoint of the line joining their feet, their tops subtend 30° and 60°. Then x:y is:

A. 1:2B. 2:1C. 1:3D. 3:1

Useful Resource: Ravi Test Papers

Q10. If the sun's altitude is 60°, the height of a tower casting a 30 m shadow is:

A. 30√3 mB. 15 mC. 30/√3 mD. 15√2 m

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Test 4

Applications of Trigonometry

10 Questions

Q1. An observer 1.5 m tall is 28.5 m from a tower. The angle of elevation of the top from the observer's eye is 45°. The tower height is:

A. 27 mB. 30 mC. 28.5 mD. None of these

Q2. A 100 m tower has its sun angle change from 30° to 45°. The decrease in shadow length is:

A. 100 mB. 100√3 mC. 100(√3−1) mD. 100(√3+1) m

Q3. The instrument used for measuring angles of elevation and depression is a:

A. MicroscopeB. TelescopeC. PeriscopeD. Theodolite

Useful Resource: CBSE Class 10 Maths

Q4. From a point 15 m from a tower, the angle of elevation is 60°. The tower height is:

A. 10 mB. 10√3 mC. 20√3 mD. 15√3 m

Q5. From a point P, the angle of elevation of a 100 m tower is 30°. The distance from P to the foot of the tower is:

A. 300√3 mB. 150√3 mC. 200√3 mD. 100√3 m

Q6. If the angles of elevation from points at distances a and b are complementary, the tower height is:

A. 2√abB. √abC. abD. None of these

Useful Resource: CBSE Class 10 Science

Q7. A pole 10 m high casts a 10 m shadow. The sun's elevation is:

A. 15°B. 45°C. 30°D. 60°

Q8. A point is 75 m from a tower's foot and the angle of elevation of the top is 60°. The tower height is:

A. 75√3 mB. 75 mC. 75/√3 mD. 150 m

Q9. When the sun's elevation changes from 30° to 60°, the difference in shadow lengths of a 15 m pole is:

A. 7.5 mB. 15 mC. 10√3 mD. 5√3 m

Useful Resource: CBSE Class 10 English

Q10. Walking x metres towards a chimney changes the angle of elevation from 30° to 60°. If the chimney height is h, then x is:

A. h(√3−1/√3)B. h(√3+1/√3)C. h/√3D. √3h

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Test 5

Applications of Trigonometry

10 Questions

Q1. The height of a tower whose top is observed at 45° from a point 50 m away is:

A. 50√3 mB. 50 mC. 50/√2 mD. 50/√3 m

Q2. The distance of a car from a 150 m tower when the angle of depression is 30° is:

A. 50√3 mB. 150√3 mC. 150√2 mD. 75 m

Q3. The distance of a boat from the foot of a 300 m cliff when the angle of depression is 60° is:

A. 100√3 mB. 300√3 mC. 100 mD. 300 m

Useful Resource: CBSE Class 10 Social Science

Q4. A man walks a distance equal to twice the height of a pole and the angle of elevation changes from α to 2α. Then α is:

A. 30°B. 15°C. 60°D. 45°

Q5. Two ships are 100 m apart. Their angles of depression from a lighthouse top are 45° and 30° on the same side. The lighthouse height is:

A. 50 mB. 50(√3−1) mC. 50(√3+1) mD. 100 m

Q6. A slide has its top 1.5 m high and is inclined at 30° to the ground. Its length is:

A. √3 mB. 3 mC. 1.5 mD. 2√3 m

Useful Resource: CBSE Class 10 All Subjects

Q7. A tower's shadow is 30 m at a sun elevation of 30°. At 60°, its shadow is:

A. 20 mB. 10 mC. 30√3 mD. 10√3 m

Q8. The height of a cloud above a lake can be found using its reflection and angles of elevation/depression; in the source, the cloud height is expressed using:

A. h tan(45°+θ)B. h tan(45°−θ)C. h cot(45°+θ)D. h cot(45°−θ)

Q9. For a vertical rod and its shadow in ratio 1:√3, the tangent of the sun's elevation is:

A. √3B. 1C. 1/√3D. 2

Useful Resource: Ravi Test Papers .in

Q10. A 6 m pole has a shadow 2√3 m long. The sun's elevation is:

A. 60°B. 45°C. 30°D. 90°

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Test 6

Applications of Trigonometry

10 Questions

Q1. In a right triangle, the ratio perpendicular/base represents:

A. sinθB. cosθC. tanθD. cotθ

Q2. The ratio hypotenuse/perpendicular is represented by:

A. sinθB. cosθC. cosecθD. cotθ

Q3. The ratio base/perpendicular is represented by:

A. tanθB. cotθC. secθD. cosecθ

Useful Resource: RAVI MATHS TUITION CENTRE YouTube

Q4. The line of sight and horizontal form an angle of elevation when the object is:

A. Above the observer's horizontal levelB. Below the horizontal levelC. At the same level onlyD. Never

Q5. The angle of depression of an object is measured from the observer's:

A. Vertical lineB. Horizontal line of sightC. Ground onlyD. Tower

Q6. For an angle of elevation θ, the basic relation is tanθ =

A. Hypotenuse/BaseB. Perpendicular/BaseC. Base/PerpendicularD. Perpendicular/Hypotenuse

Useful Resource: Ravi Test Papers

Q7. If the height of a pole equals its shadow length, tanθ is:

A. 0B. 1C. √3D. 1/√3

Q8. If the height of a tower is √3 times its shadow, tanθ is:

A. 1/√3B. 1C. √3D. 3

Q9. If the shadow is √3 times the height, tanθ is:

A. √3B. 1C. 1/√3D. 3

Useful Resource: CBSE Class 10 Maths

Q10. A tower of height h has a point at horizontal distance d. If the angle of elevation is θ, then:

A. h=d sinθB. h=d tanθC. h=d cosθD. h=d cotθ

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Test 7

Applications of Trigonometry

10 Questions

Q1. A 75 m tower is viewed at 60° elevation. The horizontal distance is:

A. 25√3 mB. 75/√3 mC. 75√3 mD. 150 m

Q2. A 150 m tower is viewed at 30° elevation. The horizontal distance is:

A. 50√3 mB. 150√3 mC. 75√3 mD. 50 m

Q3. If a tower's height is 100 m and the angle of elevation is 45°, the horizontal distance is:

A. 50 mB. 100 mC. 100√3 mD. 200 m

Useful Resource: CBSE Class 10 Science

Q4. If a tower's height is 100 m and the angle of elevation is 30°, the horizontal distance is:

A. 100/√3 mB. 100√3 mC. 50√3 mD. 200 m

Q5. If a tower's height is 60 m and angle of elevation is 60°, the distance is:

A. 20√3 mB. 60√3 mC. 20 mD. 30√3 m

Q6. If a tower's height is 60 m and angle of elevation is 45°, the distance is:

A. 30 mB. 60 mC. 60√3 mD. 20√3 m

Useful Resource: CBSE Class 10 English

Q7. If a pole is 12 m high and its shadow is 4√3 m, the sun's elevation is:

A. 30°B. 45°C. 60°D. 90°

Q8. If a pole is 10√3 m high and its shadow is 10 m, the sun's elevation is:

A. 30°B. 45°C. 60°D. 75°

Q9. If a pole is 15 m high and its shadow is 15 m, the sun's elevation is:

A. 30°B. 45°C. 60°D. 90°

Useful Resource: CBSE Class 10 Social Science

Q10. If a pole is 6 m high and its shadow is 2√3 m, the sun's elevation is:

A. 30°B. 45°C. 60°D. 75°

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Test 8

Applications of Trigonometry

10 Questions

Q1. Two trees at opposite ends of a road subtend 30° and 60° at its midpoint. Their heights are in the ratio:

A. 1:1B. 1:2C. 3:1D. 1:3

Q2. A 12 m tower has complementary angles of elevation from opposite points. If one point is 16 m away, the other is:

A. 24 mB. 9 mC. 12 mD. 18 m

Q3. If two points at distances 8 m and 18 m from a tower have complementary elevation angles, the tower height is:

A. 8 mB. 12 mC. 18 mD. 16 m

Useful Resource: CBSE Class 10 All Subjects

Q4. A ramp is 1 m high and makes 30° with the ground. Its hypotenuse is:

A. 1 mB. √3 mC. 2 mD. 2√3 m

Q5. A 2 m horizontal distance and a 60° ladder angle give ladder length:

A. 2 mB. 4/√3 mC. 4 mD. 2√3 m

Q6. A 14 m ladder with a 7 m base distance has wall height:

A. 7√3 mB. 7 mC. 14 mD. 7/√3 m

Useful Resource: Ravi Test Papers .in

Q7. A 20 cm hypotenuse with angle 60° has the side opposite 60° equal to:

A. 10 cmB. 10√3 cmC. 20 cmD. 5√3 cm

Q8. For a right triangle with hypotenuse 20 cm and angle 60°, the adjacent side is:

A. 10 cmB. 10√3 cmC. 20√3 cmD. 5 cm

Q9. For a 100 m tower viewed at 30°, the distance is:

A. 100 mB. 100√3 mC. 50√3 mD. 200 m

Useful Resource: RAVI MATHS TUITION CENTRE YouTube

Q10. For a 100 m tower viewed at 60°, the distance is:

A. 100√3 mB. 100/√3 mC. 50 mD. 200 m

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Test 9

Applications of Trigonometry

10 Questions

Q1. If two angles of elevation are complementary, their tangents have product:

A. 0B. 1C. √3D. 2

Q2. For complementary angles α and β, tanα tanβ equals:

A. tan(α+β)B. 1C. 0D. √3

Q3. If one angle of elevation is 30° and the other is 60°, they are:

A. EqualB. ComplementaryC. Supplementary onlyD. Neither

Useful Resource: Ravi Test Papers

Q4. The alternate angle to an angle of depression is the corresponding:

A. Angle of elevationB. Angle at the verticalC. Right angleD. Reflex angle

Q5. If a car is seen from a tower at an angle of depression 30°, the angle of elevation from the car to the tower top is:

A. 30°B. 60°C. 90°D. 150°

Q6. If a boat is seen from a 300 m cliff at 60° depression, its horizontal distance is:

A. 100 mB. 100√3 mC. 300 mD. 300√3 m

Useful Resource: CBSE Class 10 Maths

Q7. If a 150 m tower has 30° depression, the horizontal distance is:

A. 50√3 mB. 150√3 mC. 75 mD. 150 m

Q8. If a 75 m tower has 30° depression, the horizontal distance is:

A. 25√3 mB. 75√3 mC. 50√3 mD. 75 m

Q9. A 100 m tower and a 30° elevation give a horizontal distance of:

A. 100/√3 mB. 100√3 mC. 50√3 mD. 200 m

Useful Resource: CBSE Class 10 Science

Q10. A 75 m tower and a 60° elevation give a horizontal distance of:

A. 25√3 mB. 75/√3 mC. 75√3 mD. 150 m

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Test 10

Applications of Trigonometry

10 Questions

Q1. If the sun's elevation is 45° and a pole is 10 m high, its shadow length is:

A. 5 mB. 10 mC. 10√3 mD. 20 m

Q2. If the sun's elevation is 30° and a tower is 30 m high, its shadow length is:

A. 10√3 mB. 30√3 mC. 15√3 mD. 30 m

Q3. If the sun's elevation is 60° and a pole is 12 m high, its shadow length is:

A. 12√3 mB. 4√3 mC. 6√3 mD. 4 m

Useful Resource: CBSE Class 10 English

Q4. If a tower's shadow is 30 m and the sun's elevation is 60°, the tower height is:

A. 10√3 mB. 30√3 mC. 60 mD. 15√3 m

Q5. A 100 m tower is observed at 45°. Its horizontal distance from the observer is:

A. 50 mB. 100 mC. 100√3 mD. 200 m

Q6. If two towers have equal heights and stand at equal distances from an observer, their angles of elevation are:

A. Always differentB. EqualC. ComplementaryD. 90°

Useful Resource: CBSE Class 10 Social Science

Q7. A line joining an observer's eye to the point viewed on an object is called:

A. Line of sightB. Vertical lineC. Base lineD. Shadow line

Q8. The angle between the line of sight and the horizontal when the object is above eye level is:

A. Angle of depressionB. Angle of elevationC. Right angleD. Reflex angle

Q9. A theodolite is used to measure:

A. Lengths onlyB. MassesC. Angles of elevation and depressionD. Temperature

Useful Resource: CBSE Class 10 All Subjects

Q10. If a pole's height and shadow are equal, the sun's altitude is:

A. 30°B. 45°C. 60°D. 90°

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Ravi Test Papers — Useful Links

• Ravi Test Papers
• CBSE Class 10 Maths
• CBSE Class 10 Science
• CBSE Class 10 English
• CBSE Class 10 Social Science
• CBSE Class 10 All Subjects
• Ravi Test Papers .in
• RAVI MATHS TUITION CENTRE YouTube

Correct-answer password: RAVI2026