Question

Please Help. If ∠P is given as well as the values of p, q, and r, then explain whether the Law of Sines or the Law of Cosines should be used to solve for ∠Q. Law of Cosines, two sides and the opposite angle are known Law of Cosines, all sides are known Law of Sines, two angles and an opposite side are known Law of Sines, two sides and an included angle are known

Answer 1

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.