# A triangle has sides A, B, and C. Sides A and B are of lengths 12 and 8, respectively, and the angle between A and B is (11pi)/12 . What is the length of side C?

May 19, 2017

$c = 19.8$
Law of Cosines equation is c^2 = a^2 + b^2 – 2*a*b*cos(gamma).
c^2 = 12^2 + 8^2 – 2*12*8*cos(11π/12).
c^2 = 144 + 64 – 192*(-0.966).
${c}^{2} = 393.5$ : $c = 19.8$