Pythagoras theorem formula: a² + b² = c²
The Pythagoras theorem formula is a² + b² = c².
What each letter means
- \(c\) the hypotenuse: the longest side, opposite the right angle
- \(a,\ b\) the two shorter sides
When to use it
In any right-angled triangle when you know two sides and want the third. It also gives distances between points and diagonals of boxes.
Worked examples
1. A right-angled triangle has hypotenuse 13 cm and one side 5 cm. Find the third side.
- \(b^2=13^2-5^2=169-25=144\)
Answer: \(b=12\) cm
2. The two shorter sides of a right-angled triangle are 6.5 cm and 4.2 cm. Find the hypotenuse, to 3 significant figures.
- \(c^2=6.5^2+4.2^2=42.25+17.64=59.89\)
Answer: \(c=7.74\) cm
Common mistake
Adding when you want a shorter side. To find a shorter side, subtract: a² = c² − b².
On your course
| Course | In the exam |
|---|---|
| Edexcel 4MA1 (Higher) | Not given: learn it |
| Cambridge 0580 | Not given: learn it |
From our own IGCSE Maths formula sheets, in our words. Official: Pearson's 4MA1 specification (PDF, Appendix 5) · Cambridge's 0580 syllabus (PDF).
Practise and revise
Questions
What is the Pythagoras theorem formula?
The Pythagoras theorem formula is a² + b² = c². c: the hypotenuse: the longest side, opposite the right angle; a, b: the two shorter sides.
Is the Pythagoras' theorem given in the exam?
Edexcel 4MA1 (Higher): not given: learn it. Cambridge 0580: not given: learn it. This comes from our own IGCSE Maths formula sheets; your teacher has the official booklet.
How do I know which side is the hypotenuse?
It is the longest side, and it is always opposite the right angle.
Our own wording, examples and card, checked by IGCSE Math Revision. Not produced or endorsed by Pearson Edexcel.