In triangle ABC, angle C measures $30^{\circ}$ and side AB (the length opposite to angle C) measures 10 cm. If the length of side AC is double that of side BC, what is the measure of side BC?
Use the Law of Sines, which states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant:
$$ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} $$