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GCSE Maths: 3D Trigonometry & Pythagoras

Use Pythagoras and SOHCAHTOA inside 3D solids by finding a right-angled triangle to work in. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

GeometryFoundation & HigherAQA · Edexcel · OCR · Eduqas

What you need to know

The concepts examiners test on 3d trigonometry & pythagoras, and what each one is really asking.

Find the length of a diagonal across the base of a cuboid
Find the space diagonal of a cuboid using Pythagoras twice
Identify the right-angled triangle needed for a 3D problem
Find the angle between a line and a plane

Where marks get lost

The exam technique that separates a correct method from a correct answer.

  • Trying to work in the 3D diagram instead of redrawing the triangle flat
  • Rounding the base diagonal before using it in the second step
  • Using an edge of the solid as the hypotenuse when the diagonal is longer
  • Measuring the angle to the wrong line — it is to the shadow on the plane, not to an edge

3D Trigonometry & Pythagoras questions students ask

Is 3D Trigonometry & Pythagoras on the Foundation paper?

Yes. 3D Trigonometry & Pythagoras appears at both Foundation and Higher tier, though Higher papers take it further.

What should I know before starting 3D Trigonometry & Pythagoras?

It builds on Pythagoras and Trigonometry and Properties of 3D Shapes. If those feel shaky, practise them first — 3D Trigonometry & Pythagoras questions assume them.

What is the most common mistake in 3D Trigonometry & Pythagoras?

Trying to work in the 3D diagram instead of redrawing the triangle flat.

Which exam boards cover 3D Trigonometry & Pythagoras?

All four we support — AQA, Edexcel, OCR and Eduqas. GCSE Maths subject content is set by the DfE, so the topic is common to every board; what changes is the paper structure and the grade boundaries.