Explanation:
I assume that b is the opposite side of angle B, and c is the opposite side of angle C.
so,
a = 22.5 cm
b = 18 cm
c = 13.6 cm
remember the law of cosine :
c² = a² + b² - 2ab×cos(C)
c is the side opposite of the angle C, a and b are the other 2 sides.
that works for any angle and/or side of every triangle. you only need to set c as the side opposite of a specific angle (which you set to be C), and the other 2 sides are a and b.
contrary to Pythagoras for right-angled triangles, c does not have to be a baseline or longest side.
so, I keep here the original side and angle names to make it clearer. to get angle B :
b² = a² + c² - 2ac×cos(B)
2ac×cos(B) = a² + c² - b²
cos(B) = (a²+c²-b²)/(2ac) = (22.5²+13.6²-18²)/(2×22.5×13.6) =
= (506.25+184.96-324)/612 = 367.21/612 =
= 0.60001634...
angle B = 53.12893209...° ≈ 53.13°
to get angle C :
c² = a² + b² - 2ab×cos(C)
2ab×cos(C) = a² + b² - c²
cos(C) = (a²+b²-c²)/(2ab) = (22.5²+18²-13.6²)/(2×22.5×18) =
= (506.25+324-184.96)/810 = 645.29/810 =
= 0.796654321...
angle C = 37.18820916...° ≈ 37.19°