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.