Explanation:
remember the law of cosine :
c² = a² + b² - 2ab×cosC
c being the side opposite of the angle C. a and b are the other 2 sides. that applies to all 3 angles (while adapting the sides in the formula correspondingly).
3m is the side opposite of x, 6m is the side opposite of z.
so,
3² = 6² + 5² - 2×6×5×cos(x)
9 = 36 + 25 - 60×cos(x) = 61 - 60×cos(x)
-52 = -60×cos(x)
cos(x) = -52/-60 = 13/15
6² = 3² + 5² - 2×3×5×cos(z)
36 = 9 + 25 - 30×cos(z) = 34 - 30×cos(z)
2 = -30×cos(z)
cos(z) = -2/30 = -1/15