GCSE MATHS PRACTICE

GCSE Trigonometry Questions

In a right-angled triangle, the hypotenuse is opposite the right angle. Relative to the marked reference angle, the opposite side is across from it and the adjacent side meets it but is not the hypotenuse. SOHCAHTOA means sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse and tan θ = opposite ÷ adjacent. Use degree mode; inverse sine, cosine or tangent finds an angle. These questions cover right-angled triangles only.

Updated 12 October 2026

Worked example

Find x in the right-angled triangle. Give your answer to 1 decimal place. Use degree mode.

Use the given measurements. Calculator in degree mode.

x is opposite 35° and 10 cm is the hypotenuse, so use sine.
sin 35° = x ÷ 10, so x = 10 × sin 35°.
x = 5.735… cm, which rounds to 5.7 cm.

Answer: x = 5.7 cm

Practice questions

1
Which ratio — sine, cosine or tangent — links x and 8 cm for the marked 40° angle? Write the equation.
Use the given measurements. Calculator in degree mode.
Enlarged diagram
100%Scroll to inspect when enlarged.
2
Find x. Give your answer to 1 decimal place. Use degree mode.
Use the given measurements. Calculator in degree mode.
Enlarged diagram
100%Scroll to inspect when enlarged.
3
Find x. Give your answer to 1 decimal place. Use degree mode.
Use the given measurements. Calculator in degree mode.
Enlarged diagram
100%Scroll to inspect when enlarged.
4
Find θ. Give your answer to 1 decimal place. Use degree mode.
Use the given measurements. Calculator in degree mode.
Enlarged diagram
100%Scroll to inspect when enlarged.

Show answers

1. Cosine: cos 40° = x ÷ 8
2. x = 10.4 cm
3. x = 4.9 cm
4. θ = 36.9°

Common mistakes

Misidentifying adjacent — The hypotenuse is never the adjacent side in SOHCAHTOA.
Using radians — Set the calculator to degrees for these questions.
Using a ratio instead of its inverse — To recover an angle from a ratio, use the appropriate inverse trigonometric function.

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GCSE Trigonometry Questions

Updated 12 October 2026

Worked example

Find x in the right-angled triangle. Give your answer to 1 decimal place. Use degree mode.

Use the given measurements. Calculator in degree mode.

x is opposite 35° and 10 cm is the hypotenuse, so use sine.

sin 35° = x ÷ 10, so x = 10 × sin 35°.

x = 5.735… cm, which rounds to 5.7 cm.

Answer: x = 5.7 cm

Practice questions

Which ratio — sine, cosine or tangent — links x and 8 cm for the marked 40° angle? Write the equation.

Use the given measurements. Calculator in degree mode.

Find x. Give your answer to 1 decimal place. Use degree mode.

Use the given measurements. Calculator in degree mode.

Find x. Give your answer to 1 decimal place. Use degree mode.

Use the given measurements. Calculator in degree mode.

Find θ. Give your answer to 1 decimal place. Use degree mode.

Use the given measurements. Calculator in degree mode.

Show answers

1. Cosine: cos 40° = x ÷ 8
2. x = 10.4 cm
3. x = 4.9 cm
4. θ = 36.9°

GCSE Trigonometry Questions

Worked example

Practice questions

Common mistakes

Related resources

GCSE Trigonometry Questions

Worked example

Practice questions

Common mistakes

Related resources