# A triangle has sides A, B, and C. Sides A and B are of lengths 5 and 8, respectively, and the angle between A and B is pi/12. What is the length of side C?

Nov 6, 2016

3

#### Explanation:

You'd need to use the cosine rule
${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos C$-(rearranged to find c)

${c}^{2} = {5}^{2} + {8}^{2} - 2 \times 5 \times 8 \times \cos \left(\frac{\pi}{12}\right)$

${c}^{2} = 9.000835 \ldots$

$c = \sqrt{9.00835} \ldots = 3.000139 \ldots \approx 3$