# A triangle has sides A, B, and C. Sides A and B are of lengths 8 and 3, respectively, and the angle between A and B is (pi)/8 . What is the length of side C?

Jul 12, 2018

c=sqrt(73-48sqrt(2+sqrt(2))

#### Explanation:

Using the Theorem of cosines

${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \setminus \cos \left(\setminus \gamma\right)$

with

$a = 8 , b = 3$

and $\cos \left(\frac{\pi}{8}\right) = \frac{\sqrt{2 + \sqrt{2}}}{2}$

we get

${c}^{2} = 64 + 9 - 2 \cdot 3 \cdot 8 \cdot \cos \left(\frac{\pi}{8}\right)$

c=sqrt(73-48sqrt(2+sqrt(2))