# 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 (5pi)/12 . What is the length of side C?

Jun 16, 2018

c=sqrt(34-15sqrt(2-sqrt(3))

#### Explanation:

Note that
$\cos \left(5 \cdot \frac{\pi}{12}\right) = \frac{\sqrt{3} - 1}{2 \sqrt{2}}$
and we get

${c}^{2} = 9 + 25 - 30 \cdot \frac{\sqrt{3} - 1}{2 \sqrt{2}}$
or

c=sqrt(34-15sqrt(2-sqrt(3))