GCSE Mathematics Revision — Pythagoras & Trigonometry
Revise Pythagoras & Trigonometry for GCSE Mathematics with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.
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- Pythagoras & Trigonometry in GCSE Mathematics: explanation, examples, and practice links on this page.
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Go to SOHCAHTOA ProblemsTopic explanation
What is Pythagoras & Trigonometry?
Pythagoras' theorem states that in a right-angled triangle, a² + b² = c² where c is the hypotenuse. Trigonometry uses the ratios sin, cos and tan (SOHCAHTOA) to find missing sides and angles. Label the triangle: Hypotenuse (longest side, opposite the right angle), Opposite (opposite the angle you are working with), and Adjacent (next to the angle, not the hypotenuse).
Board notes: All boards test basic Pythagoras at Foundation. Trigonometry and 3D Pythagoras are Higher only.
Step-by-step explanationWorked examples
Worked example
A right-angled triangle has sides 5 cm and 12 cm. Find the hypotenuse. c² = 5² + 12² = 25 + 144 = 169. c = √169 = 13 cm.
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Start with low-focus cards for Pythagoras & Trigonometry, then move into full exam-style practice when you want the heavier session.
Common mistakes
- 1Using Pythagoras when the triangle is not right-angled — check for the right angle first.
- 2Subtracting instead of adding when finding the hypotenuse (c² = a² + b², not a² - b²).
- 3Labelling Opposite and Adjacent incorrectly — they depend on which angle you are using.
- 4Calculator in the wrong mode (radians instead of degrees) when using trigonometry.
Pythagoras & Trigonometry exam questions
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Frequently asked questions
When do I use Pythagoras vs trigonometry?
Use Pythagoras when you know two sides and want the third side. Use trigonometry when you know one side and one angle (or two sides and want an angle).
What is SOHCAHTOA?
SOH: sin = Opposite/Hypotenuse. CAH: cos = Adjacent/Hypotenuse. TOA: tan = Opposite/Adjacent. It helps you choose the right ratio.