# A triangle has sides A, B, and C. Sides A and B are of lengths 2 and 9, respectively, and the angle between A and B is (3pi)/4 . What is the length of side C?

Jul 10, 2016

$C = 10.51$

#### Explanation:

Since, by the Carnot theorem:

${C}^{2} = {A}^{2} + {B}^{2} - 2 A B \cos \hat{A B}$

in this case

C=sqrt(2^2+9^2-2*2*9*cos3pi/4

$C = \sqrt{4 + 81 - 36 \cdot \left(- \frac{\sqrt{2}}{2}\right)}$

$C = \sqrt{85 + 18 \sqrt{2}}$

$C = 10.51$