Third Side of a Triangle Using Law of Cosines

Consider a triangle with the following properties: it has two sides measuring 8 cm and 15 cm, and the included angle between these sides is $60^{ ext{o}}$. To find the length of the third side, we can use the Law of Cosines, which states that for any triangle with sides $a$, $b$, and $c$, and an included angle $C$, the relationship is given by:

$$c^2 = a^2 + b^2 - 2ab imes ext{cos}(C)$$

In this case, let side $a = 8$, side $b = 15$, and angle $C = 60^{ ext{o}}$. What is the length of the third side?