# A triangle has sides A, B, and C. Sides A and B are of lengths 1 and 1, respectively, and the angle between A and B is (2pi)/3 . What is the length of side C?

Jul 8, 2016

$C = \sqrt{3}$

#### Explanation:

you can solve the problem by using the Carnot theorem:

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

so, in this case:

${C}^{2} = {1}^{2} + {1}^{2} - 2 \cdot 1 \cdot 1 \cos 2 \frac{\pi}{3}$

${C}^{2} = 2 - \cancel{2} \cdot \left(- \frac{1}{\cancel{2}}\right) = 3$

$C = \sqrt{3}$