For ΔPQR, p = 7 ft, q = 9 ft, and m∠R = 55°. What is m∠Q?

Answer 1

Using the Law of Cosines:

r² = 7² + 9² - 2(7)(9)cos(55°)

r² = 49 + 81 - 126cos(55°)

r² = 49 + 81 - 72.27063

r² = 57.72937

r = 7.59798

Using the Law of Sins:

sin(55°)/7.59798 = sin(Q)/9

sin(Q) = 9sin(55°)/7.59798 = 0.970306

Q = sin^-1(0.970306) = 76°