Pythagoras' theorem
In a right-angled triangle, a² + b² = c² where c is the hypotenuse.
The hypotenuse is the longest side, opposite the right angle. To find the hypotenuse: square the two shorter sides, sum them, take the square root. To find a shorter side: square hyp, subtract the known short side, square root.
Worked examples
Triangle 3, 4, c: c² = 9 + 16 = 25 ⇒ c = 5.
Triangle 5, b, 13: b² = 169 − 25 = 144 ⇒ b = 12.
3-4-5 and 5-12-13 are common Pythagorean triples.
Frequently asked questions
How do I know which side is the hypotenuse?
Always the longest side, always opposite the right angle. The right angle is marked with a small square.
Pythagorean triples?
Three whole numbers that fit. Common ones: (3,4,5), (5,12,13), (8,15,17), (7,24,25). Useful for spotting answers.