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Free · Class 10 · 5 worksheets · answer keys · practise online · set 8

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 8
Name:Date:Score:    / 8

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

  1. In △ABC, ∠B = 90°, AB = 8 cm, BC = 6 cm. Find tan A.
  2. In △ABC, ∠B = 90°, AB = 12 cm, BC = 5 cm. Find sec A.
  3. In △ABC, ∠B = 90°, AC = 39 cm, BC = 15 cm. Find sin A.
  4. In △ABC, ∠B = 90°, AB = 72 cm, BC = 21 cm. Find sin A.
  5. In △ABC, ∠B = 90°, AC = 29 cm, BC = 20 cm. Find sec A.
  6. In △ABC, ∠B = 90°, AC = 75 cm, BC = 72 cm. Find sec A.
  7. In △ABC, ∠B = 90°, AB = 10 cm, BC = 24 cm. Find cosec A.
  8. In △ABC, ∠B = 90°, AB = 15 cm, BC = 36 cm. Find sin A.

Find the other ratios

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

Solve.

  1. If sin A = 4/5, find cos A and tan A.
  2. If sin A = 20/29, find cos A and tan A.
  3. If sin A = 24/25, find cos A and tan A.
  4. If sin A = 21/29, find cos A and tan A.
  5. If tan A = 3/4, find sin A and cos A.
  6. If tan A = 20/21, find sin A and cos A.
  7. If sin A = 12/13, find cos A and tan A.
  8. If tan A = 5/12, find sin A and cos A.

Standard angles

Class 10 · Worksheet 3 · set 8
Name:Date:Score:    / 10

Find the value.

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

Simplify the identities

Class 10 · Worksheet 4 · set 8
Name:Date:Score:    / 12

Simplify.

  1. cosθ × secθ
  2. sin 60° cos 30° + cos 60° sin 30°
  3. sec²θ − tan²θ
  4. (1 + tan²θ) cos²θ
  5. sinθ / cosθ
  6. sin(90° − θ)
  7. 1 + cot²θ
  8. sinθ × cosecθ
  9. cosec²θ − cot²θ
  10. (1 − cos²θ) cosec²θ
  11. cos(90° − θ)
  12. (1 − sin²θ) sec²θ

Heights and distances

Class 10 · Worksheet 5 · set 8
Name:Date:Score:    / 6

Solve. Draw a figure first.

  1. A kite is flying on a string 28 m long. The string makes an angle of 30° 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 45° with the ground. Find the height of the kite.
  3. A tower is 6 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. From a point 54 m from the foot of a tower, the angle of elevation of its top is 45°. Find the height of the tower.
  5. From a point 15 m from the foot of a tower, the angle of elevation of its top is 30°. Find the height of the tower.
  6. A tower is 33 m tall. The angle of elevation of its top from a point on the ground is 45°. 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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