Pythagoras & Trigonometry — GCSE Mathematics Revision
Revise Pythagoras & Trigonometry for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to SOHCAHTOA ProblemsWhat 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 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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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
Exam-style questions for Pythagoras & Trigonometry with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Pythagoras & Trigonometry
Core concept
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 th…
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.