Finding the Length of Side BC in Triangle ABC

Consider a triangle ABC where the lengths of sides AB and AC are 8 and 6 units, respectively. The angle between these two sides, ∠BAC, measures 60 degrees. Calculate the length of side BC.

Use the Law of Cosines, which states that for any triangle with sides of lengths $a$, $b$, and $c$, opposite the angles $A$, $B$, and $C$, respectively, the following holds: $$c^2 = a^2 + b^2 - 2ab imes ext{cos}(C)$$. In our case, let $a = 8$, $b = 6$, and $C = 60^{ ext{o}}$.