In the triangle shown on the right, ÐP = 55°, n = 10, and g = 12. Find the remaining side and the two angles. Round all answers to the nearest tenth. Length of side p =

p = 10.3

m∠N = 52.7°

m∠G = 72.3°

Step-by-step explanation:

In ΔPNG

∵ m∠P = 55°

∵ n = 10 and g = 12

By using cos Rule:

∵ p² = n² + g² - 2 (n) (g) cosP

∴ p² = 100 + 144 - 2 (10) (12) cos (55°) = 106.341655

∴ p = 10.3

By using sin Rule:

10/sin (N) = 12/sin (G) = 10.3/sin55

∴ sinN = 10 (sin55) / 10.3 = 0.7952932

∴ m∠N = 52.7°

∴ sinG = 12 (sin55) / 10.3 = 0.95435189

∴ m∠G = 72.3°