IGCSE Maths / Pythagoras theorem
Pythagoras: finding the hypotenuse
Edexcel International GCSE Maths (4MA1), chapter 15: Pythagoras theorem, specification point 4.8a-f. Free lesson.
Read the revision notes · IGCSE Maths past papers
Pythagoras’ theorem finds the hypotenuse of a right-angled triangle by squaring and adding the two shorter sides. You must take the square root at the end, because the rule gives you the hypotenuse squared.
How to identify the hypotenuse
The hypotenuse is opposite the right angle. It is always the longest side and the only side that does not touch the right angle. In Pythagoras’ theorem, this side is labelled c. The two shorter sides are labelled a and b. Either short side can be a or b, because their squares are added.
What Pythagoras’ theorem tells you
The theorem is a² + b² = c². Squaring the two short sides and adding them gives you the square of the hypotenuse, not the hypotenuse itself. Use the same unit for all three side lengths. Pythagoras’ theorem is not on the Edexcel formula sheet, so you need to remember it. You can use Pythagoras only when the triangle has a right angle. Knowing two sides of a triangle is not enough if you do not know it is right-angled. If there is no right angle, you need the sine rule or cosine rule instead.
How to find the hypotenuse
Substitute the two short side lengths into the theorem. Work out their squares, add them, then take the square root to find c.
When to round your answer
Some totals are not square numbers, so the square root is not a whole number. Keep the exact root until the final line, then round the answer as requested. Rounding early can lose accuracy marks. For 3 significant figures, round only the final answer to 3 significant figures.