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

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 5
Name:Date:Score:    / 8

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

  1. In △ABC, ∠B = 90°, AB = 40 cm, BC = 42 cm. Find tan A.
  2. In △ABC, ∠B = 90°, AB = 5 cm, BC = 12 cm. Find cot A.
  3. In △ABC, ∠B = 90°, AC = 10 cm, BC = 8 cm. Find sin A.
  4. In △ABC, ∠B = 90°, AC = 50 cm, BC = 14 cm. Find sec A.
  5. In △ABC, ∠B = 90°, AC = 58 cm, BC = 42 cm. Find sec A.
  6. In △ABC, ∠B = 90°, AB = 20 cm, BC = 21 cm. Find cos A.
  7. In △ABC, ∠B = 90°, AC = 34 cm, BC = 16 cm. Find cosec A.
  8. In △ABC, ∠B = 90°, AC = 15 cm, BC = 9 cm. Find cos A.

Find the other ratios

Class 10 · Worksheet 2 · set 5
Name:Date:Score:    / 8

Solve.

  1. If sin A = 3/5, find cos A and tan A.
  2. If sin A = 20/29, find cos A and tan A.
  3. If sin A = 7/25, find cos A and tan A.
  4. If tan A = 3/4, find sin A and cos A.
  5. If tan A = 5/12, find sin A and cos A.
  6. If sin A = 5/13, find cos A and tan A.
  7. If sin A = 15/17, find cos A and tan A.
  8. If tan A = 24/7, find sin A and cos A.

Standard angles

Class 10 · Worksheet 3 · set 5
Name:Date:Score:    / 10

Find the value.

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

Simplify the identities

Class 10 · Worksheet 4 · set 5
Name:Date:Score:    / 12

Simplify.

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

Heights and distances

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

Solve. Draw a figure first.

  1. A kite is flying on a string 24 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 20 m long. The string makes an angle of 30° with the ground. Find the height of the kite.
  3. A ladder 16 m long leans against a wall, making an angle of 30° with the ground. How high up the wall does it reach?
  4. 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.
  5. A ladder 4 m long leans against a wall, making an angle of 45° with the ground. How high up the wall does it reach?
  6. From a point 24 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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