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Free · Class 10 · 5 worksheets · answer keys · practise online · set 21

Trigonometry worksheets — Class 10, with answers

Free Class 10 trigonometry worksheets: trigonometric ratios, find other ratios, standard angle values, simplifying trig identities and heights and distances (applications) — with answers.

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Trigonometric ratios (Class 10)Find the other ratios (Class 10)Standard angles (Class 10)Simplify the identities (Class 10)Heights and distances (Class 10)

Trigonometric ratios

Class 10 · Worksheet 1 · set 21
Name:Date:Score:    / 8

Find the ratio (use Pythagoras for the missing side).

  1. In △ABC, ∠B = 90°, AC = 13 cm, BC = 5 cm. Find cos A.
  2. In △ABC, ∠B = 90°, AB = 8 cm, BC = 6 cm. Find tan A.
  3. In △ABC, ∠B = 90°, AC = 39 cm, BC = 15 cm. Find cot A.
  4. In △ABC, ∠B = 90°, AC = 13 cm, BC = 12 cm. Find tan A.
  5. In △ABC, ∠B = 90°, AB = 40 cm, BC = 42 cm. Find sin A.
  6. In △ABC, ∠B = 90°, AC = 34 cm, BC = 16 cm. Find cos A.
  7. In △ABC, ∠B = 90°, AC = 15 cm, BC = 12 cm. Find cot A.
  8. In △ABC, ∠B = 90°, AB = 15 cm, BC = 36 cm. Find tan A.

Find the other ratios

Class 10 · Worksheet 2 · set 21
Name:Date:Score:    / 8

Solve.

  1. If sin A = 24/25, find cos A and tan A.
  2. If tan A = 12/5, find sin A and cos A.
  3. If tan A = 4/3, find sin A and cos A.
  4. If tan A = 15/8, find sin A and cos A.
  5. If sin A = 4/5, find cos A and tan A.
  6. If sin A = 5/13, find cos A and tan A.
  7. If sin A = 12/13, find cos A and tan A.
  8. If tan A = 24/7, find sin A and cos A.

Standard angles

Class 10 · Worksheet 3 · set 21
Name:Date:Score:    / 10

Find the value.

  1. 2 tan 45° + 2 cot 45° =
  2. 2 cos 60° + 2 sin² 30° =
  3. 2 tan² 60° − 2 sin² 45° =
  4. cos 60° + tan 45° =
  5. 2 sin² 60° − 3 cosec² 60° =
  6. 2 sin² 30° + tan 45° + cot 45° =
  7. 3 cot 45° + 3 sin² 60° + 3 sin² 30° =
  8. 3 cot 45° − 2 sin² 30° + cos² 60° =
  9. 2 cos² 45° + 2 cot 45° + sec 60° =
  10. 3 cosec 30° + 3 tan 45° =

Simplify the identities

Class 10 · Worksheet 4 · set 21
Name:Date:Score:    / 12

Simplify.

  1. (1 − cos²θ) cosec²θ
  2. tanθ × cotθ
  3. cosθ tanθ
  4. sin 18° / cos 72°
  5. (1 + tan²θ) cos²θ
  6. (secθ + tanθ)(secθ − tanθ)
  7. tan 26° / cot 64°
  8. sin(90° − θ)
  9. sec²θ − tan²θ
  10. 1 + tan²θ
  11. cos(90° − θ)
  12. cosec²θ − cot²θ

Heights and distances

Class 10 · Worksheet 5 · set 21
Name:Date:Score:    / 6

Solve. Draw a figure first.

  1. A ladder 30 m long leans against a wall, making an angle of 30° with the ground. How high up the wall does it reach?
  2. A tower is 24 m tall. The angle of elevation of its top from a point on the ground is 60°. How far is the point from the foot of the tower?
  3. A ladder 24 m long leans against a wall, making an angle of 60° with the ground. How high up the wall does it reach?
  4. A tower is 24 m tall. The angle of elevation of its top from a point on the ground is 30°. How far is the point from the foot of the tower?
  5. A tower is 57 m tall. The angle of elevation of its top from a point on the ground is 45°. How far is the point from the foot of the tower?
  6. A ladder 10 m long leans against a wall, making an angle of 45° with the ground. How high up the wall does it reach?

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Questions

How do I remember the trigonometric values?

Write 0, 1, 2, 3, 4 under 0°, 30°, 45°, 60°, 90°, divide each by 4 and take the square root — that gives sin. Write the same list backwards for cos.

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