Law of Cosines, Sines and Tangents

The law of cosines is a generalization of the Pythagorean theorem to general triangles (which need not be necessarily right triangles):

a² = b² + c² - 2bccos a
b² = a² + c² - 2accos b
c² = a² + b² - 2abcos g

The ratios of the lengths of the sides is corresponding to the ratio of the opposite angles:

a : b : c = sin a : sin b : sin g
,
with R being the radius of the circumcircle.