Triangle Side Length Calculation

In triangle ABC, the side lengths are given as $a$, $b$, and $c$, with the respective angles opposite these sides denoted as $A$, $B$, and $C$. If angle A is $45^{ ext{°}}$, angle B is $60^{ ext{°}}$, and the length of side a is $10$ units, what is the length of side c, opposite angle C?

To solve this, you can employ the Law of Sines, which states:

$$ \f\frac{a}{\sin(A)} = \f\frac{b}{\sin(B)} = \f\frac{c}{\sin(C)} $$

First, find angle C, and then apply the law to find the length of side c.