A 13 m ladder leans against a wall. Its foot is 5 m away from the wall. How high up the wall does the ladder reach?

In a **right** triangle, the square of the hypotenuse equals the sum of the squares of the other two sides:

hypotenus$e^2$ = side₁² + side₂²

Classic Pythagorean triple: 3, 4, 5 — because $3^2+4^2=9+16=25=5^2$.

Other triples to recognise: (5, 12, 13), (8, 15, 17), (7, 24, 25). The rule only applies when one of the angles is 90°. Never use Pythagoras for non-right triangles.