How to Use the Pythagorean Theorem

a^{2} + b^{2} = c^{2}

Here $a$ and $b$ are the legs, and $c$ is the hypotenuse, the longest side across from the right angle.

Worked examples

$6^{2} + 8^{2} = c^{2}$ , so $c^{2} = 100$ .

$c = 10$

$5^{2} + b^{2} = 1 3^{2}$

$b^{2} = 169 - 25 = 144$ , so $b = 12$ .

The horizontal change is 3 and the vertical change is 4.

$d = 3^{2} + 4^{2} = 5$

A leg is 5 and the hypotenuse is 13, so the other leg is $5^{2} + 1 3^{2}$ .

That makes a leg longer than the hypotenuse, which is impossible. When you're finding a leg, subtract: $1 3^{2} - 5^{2} = 12$ .

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