Answer:
x ≈ 88°
Step-by-step explanation:
using the Cosine rule in Δ ABC
cos C = [tex]\frac{a^2+b^2-c^2}{2ab}[/tex]
a, b, c are the sides opposite angles A, B and C
here a = 10, b = 7, c = 12 and ∠ C = x , then
cos x = [tex]\frac{10^2+7^2-12^2}{2(10)(7)}[/tex] = [tex]\frac{100+49-144}{140}[/tex] = [tex]\frac{5}{140}[/tex] , then
x = [tex]cos^{-1}[/tex] ( [tex]\frac{5}{140}[/tex] ) ≈ 88° ( to the nearest degree )
