# How do you solve for the missing side of a right triangle given a = 24 and b = 45?

Jul 7, 2016

$c = 51$

#### Explanation:

Pythagorean theorem: ${a}^{2} + {b}^{2} = {c}^{2}$
This theorem works with all right triangles.

We are given $a$ and $b$. Let's plug these into the formula.

${\left(24\right)}^{2} + {\left(45\right)}^{2} = {c}^{2}$

$576 + 2025 = {c}^{2}$

$2601 = {c}^{2}$

$51 = c$

We found $c$, or the length of the missing side, to be $51$.
We can check by plugging all of these values back into the formula and making sure they match up.

$576 + 2025 = 2601$

$2601 = 2601$