Triangle ABC has altitude h. B C a h x A D b y C Move the options to the spaces to complete the proof of the Law of Cosines. , which becomes By the definition of cosine and multiplication, y = a cos C. Then, by subtraction and substitution, x=b-a cos C. By the definition of sine and multiplication, ha sin C. By the Pythagorean Theorem, c = by substitution. By the distributive property, the equation becomes which factors to By the Pythagorean Identity, the final equation is h+x =a+b-2ab cos C c2 = (asinC) + (b-a cos C) a (sin C+ cos C) + b-2ab cos C a sin C+b2-2ab cos C+ a cos C