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

Dec 1, 2016

#### Answer:

C = sqrt(153+9sqrt(2)(sqrt(3)+1)

#### Explanation:

The law of cosine states that:

${C}^{2} = {A}^{2} + {B}^{2} - 2 A B \cos \left(A \angle B\right)$

So:

$C = \sqrt{{12}^{2} + {3}^{2} + 3 \cdot 12 \cdot \cos \left(\frac{\pi}{12}\right)}$

C = sqrt(144+9+36sqrt(2)/4(sqrt(3)+1)

C = sqrt(153+9sqrt(2)(sqrt(3)+1)