# A triangle has sides A, B, and C. Sides A and B are of lengths 2 and 3, respectively, and the angle between A and B is (3pi)/4 . What is the length of side C?

Dec 22, 2015

${c}^{2} = 13 - \frac{12}{\sqrt{2}}$
The triangle image would be as shown above. To find c, use $\cos C = \frac{{a}^{2} + {b}^{2} - {c}^{2}}{2 a b}$. Accordingly,
$\cos \left(\frac{\pi}{4}\right) = \frac{4 + 9 - {c}^{2}}{12}$
${c}^{2} = 13 - \frac{12}{\sqrt{2}}$