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°