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Free · Class 10 · 5 worksheets · answer keys · practise online · set 65

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 65
Name:Date:Score:    / 8

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

  1. In △ABC, ∠B = 90°, AB = 12 cm, BC = 9 cm. Find sin A.
  2. In △ABC, ∠B = 90°, AC = 87 cm, BC = 60 cm. Find tan A.
  3. In △ABC, ∠B = 90°, AB = 6 cm, BC = 8 cm. Find cos A.
  4. In △ABC, ∠B = 90°, AC = 39 cm, BC = 15 cm. Find sec A.
  5. In △ABC, ∠B = 90°, AB = 8 cm, BC = 15 cm. Find tan A.
  6. In △ABC, ∠B = 90°, AC = 87 cm, BC = 63 cm. Find tan A.
  7. In △ABC, ∠B = 90°, AC = 29 cm, BC = 21 cm. Find cot A.
  8. In △ABC, ∠B = 90°, AC = 58 cm, BC = 42 cm. Find sin A.

Find the other ratios

Class 10 · Worksheet 2 · set 65
Name:Date:Score:    / 8

Solve.

  1. If tan A = 20/21, find sin A and cos A.
  2. If sin A = 8/17, find cos A and tan A.
  3. If sin A = 7/25, find cos A and tan A.
  4. If sin A = 3/5, find cos A and tan A.
  5. If sin A = 5/13, find cos A and tan A.
  6. If sin A = 12/13, find cos A and tan A.
  7. If sin A = 15/17, find cos A and tan A.
  8. If tan A = 12/5, find sin A and cos A.

Standard angles

Class 10 · Worksheet 3 · set 65
Name:Date:Score:    / 10

Find the value.

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

Simplify the identities

Class 10 · Worksheet 4 · set 65
Name:Date:Score:    / 12

Simplify.

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

Heights and distances

Class 10 · Worksheet 5 · set 65
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 45° with the ground. Find the height of the kite.
  2. A ladder 30 m long leans against a wall, making an angle of 45° with the ground. How high up the wall does it reach?
  3. A tower is 27 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?
  4. A kite is flying on a string 4 m long. The string makes an angle of 30° with the ground. Find the height of the kite.
  5. A kite is flying on a string 22 m long. The string makes an angle of 60° with the ground. Find the height of the kite.
  6. From a point 54 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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