Working Backwards

The theorem also finds a leg when you know the hypotenuse and the other leg. The hypotenuse square is the biggest, so take the known leg's square away from it.

Here ${5}^{2}+{b}^{2} = {13}^{2}$, so ${b}^{2} = 169-25 = 144$, and the leg is 12. The usual slip is to add the squares, which would give a leg longer than the hypotenuse. A leg is always shorter than the hypotenuse, so check that.