In triangle ABC, the lengths of sides AB and AC are represented as follows:
Side AB measures $10$ cm, and side AC measures $12$ cm.
If the angle opposite side BC measures $60$ degrees, what is the length of side BC?
Use the Law of Cosines, which states that for any triangle with sides $a$, $b$, and $c$, and corresponding opposite angles $A$, $B$, and $C$:
$$c^2 = a^2 + b^2 - 2ab \cdot \cos(C)$$