# A triangle has sides A, B, and C. Sides A and B are of lengths 1 and 4, respectively, and the angle between A and B is pi/12. What is the length of side C?

Jan 1, 2018

$c \approx 3.045$

#### Explanation:

From the Law of Cosines we know that:

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

Solving for $c$ we have:

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

Substituting we have:

$c = \sqrt{{1}^{2} + {4}^{2} - 2 \left(1\right) \left(4\right) \cos \left(\frac{\pi}{12}\right)} \approx 3.045$