# A triangle has sides A, B, and C. Sides A and B are of lengths 4 and 5, respectively, and the angle between A and B is (pi)/8 . What is the length of side C?

Mar 4, 2016

$c = \sqrt{{a}^{2} + {b}^{2} - 2 a b \cos C} = \sqrt{{4}^{2} + {5}^{2} - 2 \left(4\right) \left(5\right) \cos \left(\frac{\pi}{8}\right)} \approx 2.01$

#### Explanation:

Use the law of cosines and then substitute in the values for a, b, and angle C and then find side c.