# A triangle has sides A, B, and C. Sides A and B are of lengths 3 and 7, respectively, and the angle between A and B is pi/6. What is the length of side C?

Jul 8, 2017

The length is $= 4.65 u$

#### Explanation:

The side $A = 3$

The side $B = 7$

The angle between $A$ and $B$ is $= \frac{1}{6} \pi$

We apply the cosine rule to the triangle

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

$= {3}^{2} + {7}^{2} - 2 \cdot 3 \cdot 7 \cdot \cos \left(\frac{1}{6} \pi\right)$

$= 9 + 49 - 42 \cos \left(\frac{1}{6} \pi\right)$

$= 21.6$

$C = \sqrt{21.6} = 4.65$