Do I need an account to practise 3D trigonometry?

No. You can start practising 3D trigonometry straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.

Pythagoras' theorem and trigonometry

3D trigonometry

11 self-marking GCSE and IGCSE practice questions on 3D trigonometry, written specifically for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Higher and Extended tier. Instant marking with full worked solutions on every question.

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Sample 3D trigonometry questions

A few of the 11 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

Question 13 marksGrade 8-9
The length of a diagonal of a cuboid is 20 cm. The diagonal makes an angle of 24° with the base. The area of the base is 150 cm². Work out the volume of the cuboid, correct to 3 significant figures.
Show the worked solution
The angle between the space diagonal and the base is opposite the cuboid's VERTICAL HEIGHT. M1
Height $=20\sin(24°)=8.135$ cm M2
Volume $=\text{base area}\times\text{height}=150\times8.135=1220$

What are the common mistakes in 3D trigonometry?

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

Swaps the opposite and adjacent sides in a right-angled triangle
Swapped opposite and adjacent (used base diagonal ÷ height instead of height ÷ base diagonal) relative to the required angle
Applies a trig ratio directly to 3D edges without first identifying the correct right-angled triangle within the solid
Used the length (11 cm) directly as the adjacent side instead of first finding the base diagonal - the angle to the base is measured against the base *diagonal*, not a single edge
Uses a cuboid's edge directly in a 3D trig calculation instead of first finding the base diagonal
Forgets to first work out the base diagonal (10 cm) and instead uses the 6 cm side directly with the height, giving tan⁻¹(10/6) = 59.0° instead of tan⁻¹(10/10) = 45°.

Quick answers about 3D trigonometry

How many 3D trigonometry practice questions are there?: There are 11 self-marking GCSE and IGCSE Maths questions on 3D trigonometry, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Higher and Extended tier. Each one is marked instantly and has a full worked solution.
Do I need an account to practise 3D trigonometry?: No. You can start practising 3D trigonometry straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.