To solve for x, we can apply the Law of Cosines, which states that:
c^2 = a^2 + b^2 - 2ab*cos(C), where c is the side opposite angle C.
In this case, we want to find the length of x, which is the side opposite the given angle X = 147°. So we have:
x^2 = 6^2 + 3.6^2 - 2*6*3.6*cos(147°)
x^2 = 36 + 12.96 - 43.2*(-0.76604) (converting cos(147°) to decimal)
x^2 = 49.918
x ≈ 7.07 inches (rounded to the nearest 10th of an inch)