# A triangle has sides A, B, and C. Sides A and B are of lengths 5 and 3, respectively, and the angle between A and B is (pi)/8 . What is the length of side C?

Apr 2, 2018

color(purple)(c = sqrt(6.2836) ~~ 2.5 " units"

#### Explanation:

Given $a = 5 , b = 3 , \hat{C} = \frac{\pi}{8}$, To find side c.

Applying the Law of Cosines,

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

${c}^{2} = {5}^{2} + {3}^{2} - \left(2 \cdot 5 \cdot 3 \cdot \cos \left(\frac{\pi}{8}\right)\right) = 6.2836$

color(purple)(c = sqrt(6.2836) = 2.5 " units"