Question

In triangle PQR with side p across from angle P, side q across from angle Q, and side r across from angle R, if ∠P = 27°, ∠R = 135°, and p = 9.5, which length can be found using the Law of Sines: p, r, or RQ?

Answer 1

Using the Law of Sines and given values for angles P and R, and side length p, we can determine the length of side r opposite to angle R in triangle PQR.

Step-by-step explanation:

Given a triangle PQR with side p opposite angle P, side q opposite angle Q, and side r opposite angle R, and the values of angles P and R, and the length of side p, we can find the length of side r using the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is the same for all three sides and angles in a triangle. Specifically, p/sin(P) = q/sin(Q) = r/sin(R). Since we are given ∠P = 27°, ∠R = 135°, and p = 9.5, we can find angle Q by understanding that the sum of angles in a triangle is 180 degrees. So, ∠Q = 180° - 27° - 135°. After finding angle Q, we can rearrange the Law of Sines to solve for side r, which is the length across from angle R. However, we cannot find the length labeled RQ (side q) without additional information because it requires knowledge of either angle Q or another side length for comparison.