#### Answer

The length of the unknown side is $3\sqrt{5}$.

#### Work Step by Step

In the formula $a^2 + b^2 = c^2$, $c$ is the hypotenuse. Here, $a = 6$ and $b = 3$. We solve for c, the hypotenuse. Then $a^2 + b^2 = c^2$ becomes
$6^2 +3^2 =c^2$
$36+9 =45$
$c^2 = 45$
$c = \sqrt{45} =\sqrt{9*5} = 3\sqrt5$