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Free · Class 10 · 5 worksheets · answer keys · practise online · set 14

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 14
Name:Date:Score:    / 8

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

  1. In △ABC, ∠B = 90°, AB = 63 cm, BC = 60 cm. Find cos A.
  2. In △ABC, ∠B = 90°, AC = 17 cm, BC = 8 cm. Find sin A.
  3. In △ABC, ∠B = 90°, AC = 51 cm, BC = 24 cm. Find tan A.
  4. In △ABC, ∠B = 90°, AC = 25 cm, BC = 7 cm. Find cosec A.
  5. In △ABC, ∠B = 90°, AB = 24 cm, BC = 10 cm. Find sin A.
  6. In △ABC, ∠B = 90°, AC = 87 cm, BC = 63 cm. Find cosec A.
  7. In △ABC, ∠B = 90°, AB = 7 cm, BC = 24 cm. Find sin A.
  8. In △ABC, ∠B = 90°, AB = 14 cm, BC = 48 cm. Find cosec A.

Find the other ratios

Class 10 · Worksheet 2 · set 14
Name:Date:Score:    / 8

Solve.

  1. If tan A = 3/4, find sin A and cos A.
  2. If sin A = 24/25, find cos A and tan A.
  3. If sin A = 8/17, find cos A and tan A.
  4. If sin A = 20/29, find cos A and tan A.
  5. If tan A = 5/12, find sin A and cos A.
  6. If sin A = 3/5, find cos A and tan A.
  7. If tan A = 4/3, find sin A and cos A.
  8. If tan A = 21/20, find sin A and cos A.

Standard angles

Class 10 · Worksheet 3 · set 14
Name:Date:Score:    / 10

Find the value.

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

Simplify the identities

Class 10 · Worksheet 4 · set 14
Name:Date:Score:    / 12

Simplify.

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

Heights and distances

Class 10 · Worksheet 5 · set 14
Name:Date:Score:    / 6

Solve. Draw a figure first.

  1. A kite is flying on a string 10 m long. The string makes an angle of 60° with the ground. Find the height of the kite.
  2. A tower is 51 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?
  3. A tower is 42 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?
  4. A ladder 6 m long leans against a wall, making an angle of 45° with the ground. How high up the wall does it reach?
  5. From a point 6 m from the foot of a tower, the angle of elevation of its top is 45°. Find the height of the tower.
  6. A tower is 39 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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