# Using the pythagorean theorem, how do you solve for the missing side given a = 18 and b = 16?

Feb 27, 2017

See the entire solution process below:

#### Explanation:

The Pythagorean Theorem states:

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

$c$ is the length of the hypotenuse of a right triangle.

$a$ and $b$ are the lengths of the sides of a right triangle.

Assuming the lengths of the sides given in the problem are for a right triangle you solve for $c$ by substituting and calculating $c$:

${c}^{2} = {18}^{2} + {16}^{2}$

${c}^{2} = 324 + 256$

${c}^{2} = 580$

$\sqrt{{c}^{2}} = \sqrt{580}$

$c = \sqrt{580} = 24.083$

The length of the missing side or hypotenuse is:

$\sqrt{580}$ or $24.083$ rounded to the nearest thousandth