Free · Class 10 · 5 worksheets · answer keys · practise online
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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In right △ABC (∠B = 90°): sin A = BC/AC , cos A = AB/AC , tan A = BC/AB (opposite / hypotenuse, adjacent / hypotenuse, opposite / adjacent). cosec, sec, cot are their reciprocals. Values: sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2; cos is the same list in reverse; tan 30° = 1/√3, tan 45° = 1, tan 60° = √3. Identities : sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = cosec²θ; sin(90° − θ) = cosθ.Heights and distances : height = distance × tanθ. Angle of elevation is measured upward from the horizontal.
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
Name: Date: Score: / 8
Find the ratio (use Pythagoras for the missing side).
In △ABC, ∠B = 90°, AC = 5 cm, BC = 3 cm. Find sec A. In △ABC, ∠B = 90°, AB = 3 cm, BC = 4 cm. Find cosec A. In △ABC, ∠B = 90°, AC = 10 cm, BC = 8 cm. Find cos A. In △ABC, ∠B = 90°, AC = 15 cm, BC = 9 cm. Find sin A. In △ABC, ∠B = 90°, AC = 87 cm, BC = 63 cm. Find cosec A. In △ABC, ∠B = 90°, AC = 50 cm, BC = 14 cm. Find cot A. In △ABC, ∠B = 90°, AC = 39 cm, BC = 36 cm. Find cot A. In △ABC, ∠B = 90°, AB = 36 cm, BC = 15 cm. Find cos A.
✅ Answer key — Trigonometric ratios
sec A = 5/4 cosec A = 5/4 cos A = 3/5 sin A = 3/5 cosec A = 29/21 cot A = 24/7 cot A = 5/12 cos A = 12/13 TalentJR · talentjr.in/trigonometry-worksheet
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Find the other ratios Class 10 · Worksheet 2
Name: Date: Score: / 8
Solve.
If tan A = 24/7, find sin A and cos A. If sin A = 21/29, find cos A and tan A. If sin A = 15/17, find cos A and tan A. If sin A = 20/29, find cos A and tan A. If sin A = 12/13, find cos A and tan A. If tan A = 3/4, find sin A and cos A. If tan A = 4/3, find sin A and cos A. If tan A = 8/15, find sin A and cos A.
✅ Answer key — Find the other ratios
sin A = 24/25, cos A = 7/25 cos A = 20/29, tan A = 21/20 cos A = 8/17, tan A = 15/8 cos A = 21/29, tan A = 20/21 cos A = 5/13, tan A = 12/5 sin A = 3/5, cos A = 4/5 sin A = 4/5, cos A = 3/5 sin A = 8/17, cos A = 15/17 TalentJR · talentjr.in/trigonometry-worksheet
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Standard angles Class 10 · Worksheet 3
Name: Date: Score: / 10
Find the value.
3 sin 90° + 3 tan² 30° + tan² 30° = cot 45° + cos² 45° + 3 sin² 60° = cos 0° + 2 cos² 60° + 2 cos 60° = sec² 45° + 3 sin² 30° = 2 cos² 30° + cos 0° = 2 tan² 30° + 3 cos 90° = 2 cos 90° + cos 0° + cos² 60° = 3 tan 45° − tan² 60° = 3 cosec² 60° + 2 cos² 45° − 2 cos 90° = 2 sin² 60° + 2 tan 45° =
✅ Answer key — Standard angles
13/3 15/4 5/2 11/4 5/2 2/3 5/4 0 5 7/2 TalentJR · talentjr.in/trigonometry-worksheet
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Simplify the identities Class 10 · Worksheet 4
Name: Date: Score: / 12
Simplify.
(1 − cos²θ) cosec²θ cos(90° − θ) cosec²θ − cot²θ (secθ + tanθ)(secθ − tanθ) sin(90° − θ) tan(90° − θ) sinθ × cosecθ sec²θ − tan²θ 1 + cot²θ cosθ tanθ sinθ / cosθ 1 + tan²θ
✅ Answer key — Simplify the identities
1 sinθ 1 1 cosθ cotθ 1 1 cosec²θ sinθ tanθ sec²θ TalentJR · talentjr.in/trigonometry-worksheet
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Heights and distances Class 10 · Worksheet 5
Name: Date: Score: / 6
Solve. Draw a figure first.
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. A kite is flying on a string 8 m long. The string makes an angle of 45° with the ground. Find the height of the kite. From a point 54 m from the foot of a tower, the angle of elevation of its top is 60°. Find the height of the tower. A ladder 28 m long leans against a wall, making an angle of 45° with the ground. How high up the wall does it reach? A ladder 24 m long leans against a wall, making an angle of 45° with the ground. How high up the wall does it reach? A kite is flying on a string 4 m long. The string makes an angle of 45° with the ground. Find the height of the kite.
✅ Answer key — Heights and distances
5√3 m (≈ 8.66 m) 4√2 m (≈ 5.66 m) 54√3 m (≈ 93.53 m) 14√2 m (≈ 19.8 m) 12√2 m (≈ 16.97 m) 2√2 m (≈ 2.83 m) TalentJR · talentjr.in/trigonometry-worksheet
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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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