Finding the Largest Angle in Triangle PQR

In triangle PQR, the lengths of the sides are given as follows: side PQ measures 9 units, side QR measures 12 units, and side RP measures 15 units.

Determine the measure of the largest angle in triangle PQR.

Use the Law of Cosines which states that:

$$ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) $$

where $c$ is the side opposite angle $C$, and $a$ and $b$ are the lengths of the other two sides.