#### Answer

$b=3\sqrt 5$

#### Work Step by Step

According to the Pythagorean Theorem, if $a$ and $b$ are the lengths of the shorter sides of a right triangle and $c$ is the length of the longest side, then $a^{2}+b^{2}=c^{2}$.
Therefore, $6^{2}+b^{2}=9^{2}$.
$36+b^{2}=81$
Subtract 36 from both sides.
$b^{2}=45$
Take the square root of both sides.
$b=\sqrt 45=\sqrt (9\times5)=\sqrt 9\times\sqrt5=3\sqrt 5$