# A triangle has sides A, B, and C. Sides A and B are of lengths 9 and 2, respectively, and the angle between A and B is pi/3. What is the length of side C?

Aug 10, 2016

$C = 8.2$

#### Explanation:

As per law of cosines
${C}^{2} = {A}^{2} + {B}^{2} - 2 A \times B \times \cos \left(\theta\right)$ where A=9;B=2 and theta=(pi)/3
or
${C}^{2} = {9}^{2} + {2}^{2} - 2 \times 9 \times 2 \times \cos \left(\frac{\pi}{3}\right)$
or
${C}^{2} = 81 + 4 - 36 \times \left(0.5\right)$
or
${C}^{2} = 85 - 18$
or
${C}^{2} = 67$
or
$C = \sqrt{67}$
or
$C = 8.2$