Pythagoras’ theorem
In a right-angled triangle, the square of the hypotenuse, the side opposite the right angle, equals the sum of the squares of the other two sides.
a² + b² = c²
Worked example
A ladder leans against a wall. Its foot is 3 m from the wall and it reaches 4 m up. How long is the ladder?
c² = 3² + 4² = 9 + 16 = 25, so c = 5 m.
Finding a shorter side
Rearrange to a² = c² − b². If the hypotenuse is 13 and one side is 5, then a² = 169 − 25 = 144, so a = 12.
Exam tip: The hypotenuse is always the longest side. If your answer for it comes out shorter than another side, you have added when you should have subtracted.