Answer:
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°
