GCSE MATHS
Pythagoras' theorem
How to find any side of a right-angled triangle.
The rule
In a right-angled triangle, a² + b² = c², where c is the hypotenuse: the longest side, opposite the right angle.
Finding the hypotenuse
Square the two shorter sides, add them, then square root.
Finding a shorter side
Square the hypotenuse, subtract the square of the side you know, then square root.
✏️ Worked example
The two shorter sides are 6 cm and 8 cm. Find the hypotenuse.
c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10 cm.
🧠 Test yourself
Hypotenuse 13, one side 5. Find the other side.
√(169 − 25) = √144 = 12.
Is a triangle with sides 3, 4 and 5 right-angled?
Yes, 9 + 16 = 25.
Which side is the hypotenuse?
The longest side, opposite the right angle.
Want it to stick?
Practise with quizzes, an AI study helper and a Mistake Bank that brings back what you got wrong, all free on OmniEx.
Revise this on OmniEx →