GCSE & IGCSE maths practice

Trigonometry (SOH CAH TOA) questions and answers

In a right-angled triangle, label the sides from the angle you're using: opposite, adjacent and hypotenuse. Then SOH CAH TOA: $\sin \theta = \dfrac{O}{H}$ , $\cos \theta = \dfrac{A}{H}$ , $\tan \theta = \dfrac{O}{A}$ . To find an angle, use the inverse ( $\sin^{-1}$ , $\cos^{-1}$ , $\tan^{-1}$ ). Make sure your calculator is in degrees.

8 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

Start the questions Right-triangle trigonometry: lesson Trigonometry calculator (SOHCAHTOA)

Where trigonometry (soh cah toa) comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: know the trigonometric ratios and use them to find angles and lengths in right-angled triangles in 2D. Higher only: in 3D.
Cambridge IGCSE (0580)	Core and Extended: apply Pythagoras' theorem and the sine, cosine and tangent ratios to right-angled triangles, including angles of elevation and depression.

The method

Label O, A and H from the angle.
Choose the ratio that uses the two sides involved.
Side on top: multiply. Side on the bottom: divide.
Angle: use the inverse function.

Trigonometry (SOH CAH TOA) questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

A right-angled triangle has hypotenuse 10 cm and an angle of $30°$ . Find the side opposite the $30°$ angle.

Question 2Warm-upFoundation

The hypotenuse is 12 cm and the angle is $40°$ . Find the adjacent side, to 3 significant figures.

Exam-style

Question 3Exam-styleFoundation

The adjacent side is 8 cm and the angle is $55°$ . Find the opposite side, to 3 significant figures.

Question 4Exam-styleFoundation

The opposite side is 5 cm and the adjacent side is 9 cm. Find the angle, to 1 decimal place.

Question 5Exam-styleFoundation

The opposite side is 7 cm and the hypotenuse is 12 cm. Find the angle, to 1 decimal place.

Question 6Exam-styleFoundation

The opposite side is 6 cm and the angle is $25°$ . Find the hypotenuse, to 3 significant figures.

Challenge

Question 7ChallengeFoundation

A 6 m ladder makes an angle of $70°$ with the ground. How high up the wall does it reach, to 3 significant figures?

Question 8ChallengeFoundation

A tower is 40 m tall. From a point 65 m from its base, find the angle of elevation of the top, to 1 decimal place.

Common mistakes

Calculator in radians.
Labelling from the wrong angle.
Multiplying when the unknown is the denominator (h = 6 ÷ sin 25°, not 6 × sin 25°).

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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