# Using the pythagorean theorem, how do you solve for the missing side given c = 65 and a = 56?

Apr 27, 2016

$b = 33$

#### Explanation:

Assuming $c = 65$ is the hypotenuse and $a = 56$ is one of the legs, the Pythaorgean Theorem tells us:

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

So:

${b}^{2} = {c}^{2} - {a}^{2} = {65}^{2} - {56}^{2} = 4225 - 3136 = 1089 = {33}^{2}$

Since we want $b > 0$ we want the positive square root of $1089$, namely $b = 33$.