# How do you use the pythagorean theorem to solve for the missing side given a = 5, c = 19?

Aug 24, 2017

See a solution process below:

#### Explanation:

The Pythagorean Theorem states:"

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

Where:

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

$x$ is the hypotenuse of the the right triangle.

Substituting and solving for $b$ gives:

${5}^{2} + {b}^{2} = {19}^{2}$

$25 + {b}^{2} = 361$

$25 - \textcolor{red}{25} + {b}^{2} = 361 - \textcolor{red}{25}$

$0 + {b}^{2} = 336$

${b}^{2} = 336$

$\sqrt{{b}^{2}} = \sqrt{336}$

$b = \sqrt{336}$

$b = \sqrt{16 \cdot 21}$

$b = \sqrt{16} \cdot \sqrt{21}$

$b = 4 \sqrt{21}$

Or

$b = 18.330$ rounded to the nearest thousandth.