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Free · Class 10 · 5 worksheets · answer keys · practise online · set 67

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 67
Name:Date:Score:    / 8

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

  1. In △ABC, ∠B = 90°, AB = 30 cm, BC = 16 cm. Find sin A.
  2. In △ABC, ∠B = 90°, AC = 39 cm, BC = 36 cm. Find cot A.
  3. In △ABC, ∠B = 90°, AC = 26 cm, BC = 10 cm. Find cot A.
  4. In △ABC, ∠B = 90°, AC = 39 cm, BC = 15 cm. Find sec A.
  5. In △ABC, ∠B = 90°, AB = 60 cm, BC = 63 cm. Find sin A.
  6. In △ABC, ∠B = 90°, AB = 60 cm, BC = 63 cm. Find tan A.
  7. In △ABC, ∠B = 90°, AC = 75 cm, BC = 21 cm. Find sec A.
  8. In △ABC, ∠B = 90°, AC = 26 cm, BC = 10 cm. Find sec A.

Find the other ratios

Class 10 · Worksheet 2 · set 67
Name:Date:Score:    / 8

Solve.

  1. If sin A = 3/5, find cos A and tan A.
  2. If tan A = 4/3, find sin A and cos A.
  3. If sin A = 5/13, find cos A and tan A.
  4. If sin A = 4/5, find cos A and tan A.
  5. If tan A = 21/20, find sin A and cos A.
  6. If sin A = 12/13, find cos A and tan A.
  7. If tan A = 12/5, find sin A and cos A.
  8. If sin A = 8/17, find cos A and tan A.

Standard angles

Class 10 · Worksheet 3 · set 67
Name:Date:Score:    / 10

Find the value.

  1. 3 sec 60° + 3 sec² 45° + sin 30° =
  2. 2 cos² 45° + 2 sin 30° + 2 tan 45° =
  3. 2 cos 60° + cos 60° + 2 sec 60° =
  4. 2 sin² 30° + 3 sin² 60° + 3 cot 45° =
  5. cot 45° + sec 60° =
  6. 2 sin 90° + 3 cosec² 60° =
  7. 3 sin 30° + 2 cos² 45° + 3 sec² 45° =
  8. sec² 45° + 3 tan² 30° + sec 60° =
  9. 2 tan² 30° + 2 cos 0° =
  10. 3 cosec 30° − 3 sin 90° =

Simplify the identities

Class 10 · Worksheet 4 · set 67
Name:Date:Score:    / 12

Simplify.

  1. sin²θ + cos²θ
  2. tan 26° / cot 64°
  3. sin(90° − θ)
  4. (1 − sin²θ) sec²θ
  5. (secθ + tanθ)(secθ − tanθ)
  6. (1 + tan²θ) cos²θ
  7. sinθ / cosθ
  8. sec²θ − tan²θ
  9. cosec²θ − cot²θ
  10. cosθ tanθ
  11. 1 + tan²θ
  12. tan(90° − θ)

Heights and distances

Class 10 · Worksheet 5 · set 67
Name:Date:Score:    / 6

Solve. Draw a figure first.

  1. A kite is flying on a string 14 m long. The string makes an angle of 60° with the ground. Find the height of the kite.
  2. From a point 33 m from the foot of a tower, the angle of elevation of its top is 60°. Find the height of the tower.
  3. A ladder 16 m long leans against a wall, making an angle of 60° with the ground. How high up the wall does it reach?
  4. A kite is flying on a string 16 m long. The string makes an angle of 45° with the ground. Find the height of the kite.
  5. A ladder 26 m long leans against a wall, making an angle of 30° with the ground. How high up the wall does it reach?
  6. From a point 36 m from the foot of a tower, the angle of elevation of its top is 60°. 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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