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Free · Class 10 · 5 worksheets · answer keys · practise online · set 41

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 41
Name:Date:Score:    / 8

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

  1. In △ABC, ∠B = 90°, AC = 58 cm, BC = 40 cm. Find cot A.
  2. In △ABC, ∠B = 90°, AB = 7 cm, BC = 24 cm. Find tan A.
  3. In △ABC, ∠B = 90°, AC = 26 cm, BC = 24 cm. Find tan A.
  4. In △ABC, ∠B = 90°, AC = 87 cm, BC = 63 cm. Find sin A.
  5. In △ABC, ∠B = 90°, AC = 13 cm, BC = 5 cm. Find sec A.
  6. In △ABC, ∠B = 90°, AB = 21 cm, BC = 20 cm. Find tan A.
  7. In △ABC, ∠B = 90°, AB = 7 cm, BC = 24 cm. Find sec A.
  8. In △ABC, ∠B = 90°, AC = 39 cm, BC = 15 cm. Find sin A.

Find the other ratios

Class 10 · Worksheet 2 · set 41
Name:Date:Score:    / 8

Solve.

  1. If sin A = 12/13, find cos A and tan A.
  2. If sin A = 20/29, find cos A and tan A.
  3. If tan A = 21/20, find sin A and cos A.
  4. If tan A = 5/12, find sin A and cos A.
  5. If tan A = 12/5, find sin A and cos A.
  6. If sin A = 7/25, find cos A and tan A.
  7. If sin A = 21/29, find cos A and tan A.
  8. If tan A = 3/4, find sin A and cos A.

Standard angles

Class 10 · Worksheet 3 · set 41
Name:Date:Score:    / 10

Find the value.

  1. 3 sin² 60° + cosec 30° + 2 cosec² 60° =
  2. cos 60° + cot 45° =
  3. 2 sec² 45° − cos² 30° + sin 90° =
  4. 2 sin² 30° + 2 tan² 30° =
  5. cos² 45° + 3 cosec² 60° + 3 sin² 60° =
  6. 3 cos 60° + cos² 30° + sin 30° =
  7. 3 cot 45° + cosec² 60° =
  8. cot 45° + sin 90° + 2 cos² 30° =
  9. sec 60° − 2 tan² 30° + 2 tan 45° =
  10. 3 cos² 45° + cos² 45° + 2 cos² 30° =

Simplify the identities

Class 10 · Worksheet 4 · set 41
Name:Date:Score:    / 12

Simplify.

  1. sin(90° − θ)
  2. (1 − cos²θ) cosec²θ
  3. tanθ × cotθ
  4. 1 + tan²θ
  5. tan(90° − θ)
  6. sinθ / cosθ
  7. sec²θ − tan²θ
  8. cosec²θ − cot²θ
  9. (1 − sin²θ) sec²θ
  10. (secθ + tanθ)(secθ − tanθ)
  11. sin 18° / cos 72°
  12. sin 60° cos 30° + cos 60° sin 30°

Heights and distances

Class 10 · Worksheet 5 · set 41
Name:Date:Score:    / 6

Solve. Draw a figure first.

  1. A tower is 54 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?
  2. A kite is flying on a string 30 m long. The string makes an angle of 30° with the ground. Find the height of the kite.
  3. A ladder 18 m long leans against a wall, making an angle of 30° with the ground. How high up the wall does it reach?
  4. A tower is 12 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?
  5. 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?
  6. From a point 57 m from the foot of a tower, the angle of elevation of its top is 45°. Find the height of the tower.

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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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