The law of sine and cosine compares parts of a triangle. There are many formulas for the law of cosines, however the law of sines is a ratio, which compares sin(X)/x = sin(Y)/y. The law of cosines is more complicated. The formulas for law of cosine are all variations of c^2 = a^2 + b^2 - 2abcos(C).
It is basically the pythagorean theorem, but it includes a value for an angle, which has the - 2abcos(C).
The other sides of a and b just switch around the variables. Both these laws are widely used in life appliactions, as they do not need to account for right triangles.
