Pythagoras' theorem states that in a right-angled triangle, a squared plus b squared equals c squared, where c is the hypotenuse. To find the hypotenuse, square both shorter sides, add them, then take the square root. For legs of 5cm and 12cm, the hypotenuse is 13cm.
Pythagoras’ theorem connects the three sides of any right-angled triangle: a² + b² = c², where c is the hypotenuse, the side opposite the right angle. It appears on every GCSE paper and underpins trigonometry, so it is worth knowing cold.
Adding when you should subtract. If the hypotenuse is already known, you subtract to find the missing shorter side.
Stopping at the squared value. The answer 169 is c², not c. Always take the square root.
Assuming the hypotenuse is the side drawn longest on the page. Diagrams are rarely to scale, so find the right angle instead.
Untimed practice with worked answers. Every answer is a whole number. This extra activity does not count towards your daily progress.
Only in a right-angled triangle, when you know two sides and want the third. To find an angle, or a side from an angle, use trigonometry instead.
Square both sides you know, then subtract instead of adding: a² = c² − b². Then take the square root. Check your answer is shorter than the hypotenuse.
Yes. a² + b² = c² is printed on the GCSE Maths formulae sheet for both Foundation and Higher. See the GCSE Maths formula sheet for everything that is given.
MathsDaily gives you ten fresh questions a day across the whole curriculum, with new numbers generated every morning. Questions on this topic appear regularly in the daily set, alongside a plain-English tip and a video link if you get stuck.
Start today’s 10 →Free A4 PDFs with worked answers. See every printable, Year 1 to A-level.