# Using the pythagorean theorem, how do you solve for the missing side given a = 14 and b = 13?

Apr 12, 2016

$c = \sqrt{{a}^{2} + {b}^{2}} = \sqrt{{14}^{2} + {13}^{2}} = \sqrt{365} \cong 19.1$

#### Explanation:

The Pythagorean Theorem applies to right angle triangles, where the sides $a$ and $b$ are those which intersect at right angle. The third side, the hypotenuse, is then $c$

In our example we know that $a = 14$ and $b = 13$ so we can use the equation to solve for the unknown side $c$:

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

or

$c = \sqrt{{a}^{2} + {b}^{2}} = \sqrt{{14}^{2} + {13}^{2}} = \sqrt{365} \cong 19.1$