# A triangle has sides A, B, and C. Sides A and B are of lengths 3 and 9, respectively, and the angle between A and B is pi/6. What is the length of side C?

Nov 7, 2016

$C = 3 \sqrt[2]{10 - 3 \sqrt[2]{3}}$
C=root2(A^2+B^2-2*A*B*cos(pi/6)
$C = \sqrt[2]{{3}^{2} + {9}^{2} - 2 \cdot 3 \cdot 9 \cdot \cos \left(\frac{\pi}{6}\right)}$
$C = \sqrt[2]{90 - 54 \cdot \frac{\sqrt[2]{3}}{2}} =$
$C = 3 \sqrt[2]{10 - 3 \sqrt[2]{3}}$