# A triangle has sides A, B, and C. Sides A and B are of lengths 4 and 7, respectively, and the angle between A and B is (3pi)/4 . What is the length of side C?

This question can be used using the law of cosines, and equation used to figure out information regarding either side length or angle of a non right triangle. The formula is ${c}^{2}$=${a}^{2}$ +${b}^{2}$-2(a)(b)cos($\angle C$). So plugging the info in, we get ${c}^{2}$=${4}^{2}$+${7}^{2}$-2(4)(7)cos($3 \frac{\pi}{4}$). Solving this with a calculator, we get ${c}^{2}$=102.6. Squaring that values, we get the finally of 10.1 units.