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Free · Class 10 · 5 worksheets · answer keys · practise online · set 79

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 79
Name:Date:Score:    / 8

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

  1. In △ABC, ∠B = 90°, AB = 8 cm, BC = 15 cm. Find sin A.
  2. In △ABC, ∠B = 90°, AB = 24 cm, BC = 45 cm. Find sin A.
  3. In △ABC, ∠B = 90°, AC = 26 cm, BC = 10 cm. Find sin A.
  4. In △ABC, ∠B = 90°, AB = 20 cm, BC = 21 cm. Find tan A.
  5. In △ABC, ∠B = 90°, AC = 5 cm, BC = 3 cm. Find sin A.
  6. In △ABC, ∠B = 90°, AC = 50 cm, BC = 48 cm. Find cos A.
  7. In △ABC, ∠B = 90°, AB = 24 cm, BC = 7 cm. Find cos A.
  8. In △ABC, ∠B = 90°, AC = 17 cm, BC = 15 cm. Find sin A.

Find the other ratios

Class 10 · Worksheet 2 · set 79
Name:Date:Score:    / 8

Solve.

  1. If tan A = 4/3, find sin A and cos A.
  2. If tan A = 8/15, find sin A and cos A.
  3. If tan A = 12/5, find sin A and cos A.
  4. If tan A = 24/7, find sin A and cos A.
  5. If tan A = 5/12, find sin A and cos A.
  6. If sin A = 4/5, find cos A and tan A.
  7. If sin A = 20/29, find cos A and tan A.
  8. If tan A = 7/24, find sin A and cos A.

Standard angles

Class 10 · Worksheet 3 · set 79
Name:Date:Score:    / 10

Find the value.

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

Simplify the identities

Class 10 · Worksheet 4 · set 79
Name:Date:Score:    / 12

Simplify.

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

Heights and distances

Class 10 · Worksheet 5 · set 79
Name:Date:Score:    / 6

Solve. Draw a figure first.

  1. A kite is flying on a string 6 m long. The string makes an angle of 60° with the ground. Find the height of the kite.
  2. A kite is flying on a string 8 m long. The string makes an angle of 60° with the ground. Find the height of the kite.
  3. A ladder 6 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 4 m long. The string makes an angle of 60° with the ground. Find the height of the kite.
  5. A ladder 28 m long leans against a wall, making an angle of 60° with the ground. How high up the wall does it reach?
  6. A tower is 45 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?

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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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