How do you find the missing side b given 5in 15in using the pythagorean theorem?

Feb 7, 2017

See the entire solution process below:

Explanation:

The Pythagorean Theorem states:

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

Where:

$a$ and $b$ are sides of the triangle and $c$ is the hypotenuse.

In this problem we will be solving for $b$ after substituting for $a$ and $c$. By definition the hypotenuse is always the largest value therefore we will substitute $15$ for $c$ and $5$ for $a$ giving:

${5}^{2} + {b}^{2} = {15}^{2}$

$25 + {b}^{2} = 225$

$25 - \textcolor{red}{25} + {b}^{2} = 225 - \textcolor{red}{25}$

$0 + {b}^{2} = 200$

${b}^{2} = 200$

$\sqrt{{b}^{2}} = \sqrt{200}$

$b = \sqrt{200}$ in or $b = 14.14$ in rounded to the nearest hundredth.