Consider triangle ABC. The lengths of sides AB and AC are 5 and 7 units, respectively. If angle A is 30 degrees, what is the length of side BC?
To find the length of side BC, we can use the Law of Cosines, which states that for any triangle with sides $a$, $b$, and $c$, and corresponding angles $A$, $B$, and $C$ opposite those sides, the following relationship holds:
$$c^2 = a^2 + b^2 - 2ab imes ext{cos}(C)$$
In our case, let $a = 5$, $b = 7$, and $C = 30^ ext{o}$. We want to find $c$, the length of side BC.