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Free · Class 10 · 5 worksheets · answer keys · practise online · set 39

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 39
Name:Date:Score:    / 8

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

  1. In △ABC, ∠B = 90°, AC = 17 cm, BC = 15 cm. Find cos A.
  2. In △ABC, ∠B = 90°, AC = 13 cm, BC = 12 cm. Find cot A.
  3. In △ABC, ∠B = 90°, AC = 39 cm, BC = 36 cm. Find cos A.
  4. In △ABC, ∠B = 90°, AB = 60 cm, BC = 63 cm. Find cosec A.
  5. In △ABC, ∠B = 90°, AB = 63 cm, BC = 60 cm. Find cosec A.
  6. In △ABC, ∠B = 90°, AC = 25 cm, BC = 24 cm. Find cosec A.
  7. In △ABC, ∠B = 90°, AB = 72 cm, BC = 21 cm. Find tan A.
  8. In △ABC, ∠B = 90°, AC = 50 cm, BC = 48 cm. Find tan A.

Find the other ratios

Class 10 · Worksheet 2 · set 39
Name:Date:Score:    / 8

Solve.

  1. If sin A = 4/5, find cos A and tan A.
  2. If sin A = 8/17, find cos A and tan A.
  3. If tan A = 4/3, find sin A and cos A.
  4. If sin A = 21/29, find cos A and tan A.
  5. If tan A = 7/24, find sin A and cos A.
  6. If sin A = 5/13, find cos A and tan A.
  7. If tan A = 8/15, find sin A and cos A.
  8. If tan A = 5/12, find sin A and cos A.

Standard angles

Class 10 · Worksheet 3 · set 39
Name:Date:Score:    / 10

Find the value.

  1. 3 sin² 60° + sin² 60° + 3 sin² 60° =
  2. 3 sin 30° − cos 90° + 3 cos 60° =
  3. cos 0° + 2 tan 45° =
  4. 3 tan² 60° + cosec 30° =
  5. sin 90° + cos 60° =
  6. cos² 45° + cos² 45° =
  7. tan² 60° + 2 cot 45° =
  8. 2 tan 45° + 3 sin² 45° + tan² 30° =
  9. 3 sin 90° + 2 sin 90° + 3 cos² 30° =
  10. cos² 45° + 3 sec² 45° =

Simplify the identities

Class 10 · Worksheet 4 · set 39
Name:Date:Score:    / 12

Simplify.

  1. cosθ tanθ
  2. sec²θ − tan²θ
  3. sin(90° − θ)
  4. sin 60° cos 30° + cos 60° sin 30°
  5. (1 − cos²θ) cosec²θ
  6. 1 + cot²θ
  7. sinθ / cosθ
  8. sin²θ + cos²θ
  9. sinθ × cosecθ
  10. tan(90° − θ)
  11. sin 18° / cos 72°
  12. cos(90° − θ)

Heights and distances

Class 10 · Worksheet 5 · set 39
Name:Date:Score:    / 6

Solve. Draw a figure first.

  1. A tower is 12 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?
  2. A kite is flying on a string 6 m long. The string makes an angle of 30° with the ground. Find the height of the kite.
  3. A tower is 54 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 27 m from the foot of a tower, the angle of elevation of its top is 30°. Find the height of the tower.
  6. From a point 21 m from the foot of a tower, the angle of elevation of its top is 30°. 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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