# A triangle has sides A, B, and C. Sides A and B are of lengths 3 and 1, respectively, and the angle between A and B is pi/12. What is the length of side C?

Jul 14, 2017

$c = 2.0505 u n i t s$

#### Explanation:

Use the law of cosine which is
${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos C$

$c = \sqrt{{a}^{2} + {b}^{2} - 2 a b \cos C}$
$c = \sqrt{{3}^{2} + {1}^{2} - 2 \left(3\right) \left(1\right) \cos \left(\frac{\pi}{12}\right)}$
$c = \sqrt{9 + 1 - 6 \cos \left(\frac{\pi}{12}\right)}$
$c = \sqrt{10 - 6 \cos \left(\frac{\pi}{12}\right)}$
$c = 2.0505 u n i t s$