Explanation:
law of cosine :
c² = a² + b² - 2ab×cos(C)
c being the side opposite of the angle C. a and b are the other 2 sides.
a)
x² = 7² + 9² - 2×7×9×cos(102) = 49 + 81 - 126×cos(102) =
= 130 - 126×cos(102) = 156.196873...
x = 12.49787474... ≈ 12.5
b)
9² = 5² + 12² - 2×5×12×cos(theta)
81 = 25 + 144 - 120×cos(theta)
81 = 169 - 120×cos(theta)
120×cos(theta) = 88
cos(theta) = 88/120 = 11/15 = 0.733333333...
theta = 42.83342807...° ≈ 42.8°