# A triangle has sides A, B, and C. Sides A and B are of lengths 11 and 4, respectively, and the angle between A and B is pi/6. What is the length of side C?

Mar 25, 2018

color(purple)(Length of side " c ~~ 14.06 " units"

#### Explanation:

$a = 11 , b = 4 , \hat{C} = \frac{\pi}{6}$

To find length of side $c$.

Applying law of cosines,

${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos C$

${c}^{2} = {11}^{2} + {4}^{2} - \left(2 \cdot 11 \cdot 4 \cdot \cos \left(\frac{\pi}{6}\right)\right)$

${c}^{2} = 121 + 16 - \frac{88 \cdot \sqrt{3}}{2} = 197.79$

color(purple)(Length of side " c ~~ 14.06 " units"