Question

Anyone know this ? picture shown please help

Answer 1

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.

$c^2 = a^2 + b^2 - 2ab \cos C$

We move the c² and the cosine term to their other sides,

$2ab \cos C = a^2 + b^2- c^2$

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:

$2ab \cos C = 4^2 + 5^2- 2^2 = 16 + 25 - 4 = 37$

Answer: A. 37