In a right triangle, the angle $ heta$ has a sine value of $\frac{3}{5}$. Let side $a$ be the length of the opposite side to angle $ heta$, side $b$ be the length of the adjacent side, and side $c$ be the length of the hypotenuse. If side $c$ is 10 units long, find the length of side $b$. Your answer should be the length of side $b$, expressed in simplest form.