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, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP.
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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.
Mini lesson for Pythagoras & Trigonometry
1. Understand the core idea
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.
Can you explain Pythagoras & Trigonometry without copying the notes?
2. Turn it into marks
A right-angled triangle has sides 5 cm and 12 cm. Find the hypotenuse.
Underline the method, evidence, or command-word move that would earn credit in GCSE Geometry & Measures.
3. Fix the likely mark leak
Watch for this mistake: Using Pythagoras when the triangle is not right-angled — check for the right angle first.
Write one correction rule before doing another practice question.
Practise this topic
Jump into adaptive, exam-style questions for Pythagoras & Trigonometry. Free to start; sign in to save progress.
Pythagoras & Trigonometry practice questions
These are original StudyVector questions for revision practice. They are not official exam-board questions.
Question 1
In one GCSE sentence, explain what Pythagoras & Trigonometry is testing.
Answer: 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.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Pythagoras & Trigonometry question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Using Pythagoras when the triangle is not right-angled — check for the right angle first." What should their next repair task be?
Answer: Do one Pythagoras & Trigonometry question and review the mistake type.
Mark focus: Error correction and next-step practice.
Pythagoras & Trigonometry flashcards
Core idea
What is the main idea in 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.
Common mistake
What mistake should you avoid in Pythagoras & Trigonometry?
Using Pythagoras when the triangle is not right-angled — check for the right angle first.
Practice
What is one useful practice task for Pythagoras & Trigonometry?
Answer one Pythagoras & Trigonometry question and review the mistake type.
Exam board
How should you use board notes for Pythagoras & Trigonometry?
All boards test basic Pythagoras at Foundation. Trigonometry and 3D Pythagoras are Higher only.
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, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP 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.