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Free · Class 10 · 5 worksheets · answer keys · practise online · set 17

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 17
Name:Date:Score:    / 8

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

  1. In △ABC, ∠B = 90°, AC = 10 cm, BC = 6 cm. Find sin A.
  2. In △ABC, ∠B = 90°, AB = 48 cm, BC = 14 cm. Find sec A.
  3. In △ABC, ∠B = 90°, AC = 13 cm, BC = 12 cm. Find cot A.
  4. In △ABC, ∠B = 90°, AB = 45 cm, BC = 24 cm. Find cot A.
  5. In △ABC, ∠B = 90°, AC = 29 cm, BC = 21 cm. Find cosec A.
  6. In △ABC, ∠B = 90°, AB = 30 cm, BC = 16 cm. Find cos A.
  7. In △ABC, ∠B = 90°, AC = 10 cm, BC = 8 cm. Find tan A.
  8. In △ABC, ∠B = 90°, AC = 51 cm, BC = 24 cm. Find cosec A.

Find the other ratios

Class 10 · Worksheet 2 · set 17
Name:Date:Score:    / 8

Solve.

  1. If tan A = 3/4, find sin A and cos A.
  2. If sin A = 8/17, find cos A and tan A.
  3. If sin A = 15/17, find cos A and tan A.
  4. If tan A = 8/15, find sin A and cos A.
  5. If tan A = 24/7, find sin A and cos A.
  6. If tan A = 21/20, find sin A and cos A.
  7. If sin A = 24/25, find cos A and tan A.
  8. If tan A = 15/8, find sin A and cos A.

Standard angles

Class 10 · Worksheet 3 · set 17
Name:Date:Score:    / 10

Find the value.

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

Simplify the identities

Class 10 · Worksheet 4 · set 17
Name:Date:Score:    / 12

Simplify.

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

Heights and distances

Class 10 · Worksheet 5 · set 17
Name:Date:Score:    / 6

Solve. Draw a figure first.

  1. A ladder 26 m long leans against a wall, making an angle of 60° with the ground. How high up the wall does it reach?
  2. From a point 30 m from the foot of a tower, the angle of elevation of its top is 45°. Find the height of the tower.
  3. A kite is flying on a string 12 m long. The string makes an angle of 45° with the ground. Find the height of the kite.
  4. A ladder 18 m long leans against a wall, making an angle of 60° with the ground. How high up the wall does it reach?
  5. A tower is 60 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?
  6. A kite is flying on a string 30 m long. The string makes an angle of 60° with the ground. Find the height of the kite.

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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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