Can someone please explain to me the Law of Cosines? My teacher never taught us what it meant or how to use it

Question

He is a terrible teacher and wastes about 3/4 of the class time just finding out the answers to his own practice problems

it literally takes us 35 minutes to go over like 2 simple problems

Answer 1

Draw a triangle with vertices A, B, and C. Lable side a opposite vertex A, side b opposite vertex B, and side c opposite vertex C. Then the formula for the law of cosines is c^2 = a^2 + b^2 - 2ab*cos(C). If angle C is 90 degrees, this reduces to c^2 = a^2 + b^2 - 0 = a^2 + b^2, the Pythagorean theorem.