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GCSE Maths: Pythagoras and Trigonometry

Master GCSE Maths Pythagoras theorem and trigonometry (SOH-CAH-TOA) with practice questions for both Foundation and Higher tiers. AQA, Edexcel, OCR and Eduqas.

GeometryFoundation & HigherAQA · Edexcel · OCR · Eduqas

What you need to know

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

Pythagoras theorem: a² + b² = c²
SOH-CAH-TOA for right-angled triangles
Finding missing sides and angles
Exact trigonometric values (30°, 45°, 60°)
Applications in 2D and 3D problems

Where marks get lost

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

  • Pythagoras: longest side squared = sum of other two sides squared
  • SOHCAHTOA: sin = opp/hyp, cos = adj/hyp, tan = opp/adj
  • Use inverse trig (sin⁻¹, cos⁻¹, tan⁻¹) to find angles

Pythagoras and Trigonometry questions students ask

When do I use Pythagoras vs trigonometry?

Use Pythagoras when you know two sides and want the third — no angles needed. Use trigonometry when you have an angle and need a side, or have two sides and need an angle.

What are the exact trig values I need to know?

sin 30° = ½, cos 30° = √3/2, tan 30° = 1/√3; sin 45° = cos 45° = 1/√2; sin 60° = √3/2, cos 60° = ½, tan 60° = √3.