How to Find the Hypotenuse with the Pythagorean Theorem

Right triangles · 4 minute read

If you know two sides of a right triangle, the Pythagorean theorem gives you the third.

The formula

a² + b² = c²

Here a and b are the two legs (the sides that meet at the right angle) and c is the hypotenuse, always the longest side. The theorem works only for right triangles.

Finding the hypotenuse

The legs are 6 and 8.

c² = 6² + 8² = 36 + 64 = 100
c = √100 = 10

Finding a missing leg

The hypotenuse is 13 and one leg is 5.

b² = 13² − 5² = 169 − 25 = 144
b = √144 = 12

When you look for a leg, you subtract. Subtracting the wrong way round is the most common error.

Quick checks

The hypotenuse must be longer than either leg.
Whole-number triples such as 3-4-5, 5-12-13 and 8-15-17 are handy to recognise.
Include units in the final answer.

Practice it

Practice right-triangle problems