Before using Cosine Law you have to know when to use it. Normally when we are trying to find a side or an angle with Sine Law we will have a side that is opposite to an angle, but if we dont have that, what should we do; well we use c2 = a2 + b2 – 2ab cos C which incorperates what looks to be pythagoras. What I noticed when trying to find out when trying to find out when to use pythagoras is when the sides are all next to one angle, its a dead givaway that you need to use Cosine law. If you still do not understand try watching this video by Vivid Math which helps explain when to use cosine law.
Now that we know when to use Cosine Law we can use it to solve an equation.
In the photo theres a triangle that shows two sides and one angle, if you tryed to use Sine law it wouldnt have worked, but ising the Cosine law which is c2 = a2 + b2 – 2ab cos C and fill in the blanks you would get c2 = (1.7)2 + (3.1)2 – 2(1.7)(3.1) cos 110 then the rest is algebra like what you see in the photo.