Final answer:
To solve for ∠Q, given ∠P and the sides p, q, and r, one would use the Law of Cosines, as it applies when two sides and the included angle are known.
Step-by-step explanation:
If ∠P is given along with the values of sides p, q, and r, to solve for ∠Q, you need to determine which trigonometric rule applies. The Law of Cosines should be used when you have two sides of a triangle and the angle opposite one of those sides. Specifically, the Law of Cosines is described as c² = a² + b² - 2ab cos y, which is useful when all three sides are known, or two sides and the included angle are known. Given that we have side p, side q, and ∠P, and we want to find ∠Q, we would use the Law of Cosines since we have two sides and the included angle.
In contrast, the Law of Sines is applicable when we have either two angles and a non-included side or two sides and a non-included angle. The Law of Sines states that a/sin α = b/sin β = c/sin γ. In this case, since we do not have a second angle, the Law of Sines would not be the correct method to use.