under what conditions can you use the law of sines? Explain and add an examples
You can use the law of sines sinA/a = sinB/b = sinC/c
You can only use one part of this equation, for example sinA/a = sinB/b, at a time.
A and a, and B and b are opposite one another and a and b are adjacent so if you have one side and two angles with one angle opposite the side you can use this formula, this is called SAA.
If you have two sides and an angle with one side oposite the angle you can use this formula, this is called SSA. You have to be careful with SSA because if we are given angle A, side a and b, we can get two possible angles if A is acute (< 90), and if b > a > b sin A we can get two different lengths for side c. If a < b sin A no triangle is possible.
There are examples in the widipedia article referenced below.