They're just after some straightforward algebra starting from the Law of Cosine. We don't have to evaluate any trig functions or anything like that.
[tex]c^2 = a^2 + b^2 - 2ab \cos C[/tex]
We move the c² and the cosine term to their other sides,
[tex]2ab \cos C = a^2 + b^2- c^2[/tex]
That's it for the algebra.
a,b and c are the side lengths opposite A,B and C respectively. So a=4, b=5, c=2.
We substitute:
[tex]2ab \cos C = 4^2 + 5^2- 2^2 = 16 + 25 - 4 = 37[/tex]
Answer: A. 37
