# A triangle has sides A, B, and C. Sides A and B are of lengths 8 and 1, respectively, and the angle between A and B is pi/3. What is the length of side C?

Jun 27, 2016

$C = \sqrt{57}$

#### Explanation:

By the Carnot theorem, you know that:

${C}^{2} = {A}^{2} + {B}^{2} - 2 A B \cos \gamma$

Since $A = 8 , B = 1 \mathmr{and} \gamma = \frac{\pi}{3}$:

$C = \sqrt{{8}^{2} + {1}^{2} - 2 \cdot 8 \cdot 1 \cdot \cos \left(\frac{\pi}{3}\right)}$

$C = \sqrt{65 - 16 \cdot \frac{1}{2}}$

$C = \sqrt{57}$