# A triangle has sides A, B, and C. Sides A and B are of lengths 7 and 12, respectively, and the angle between A and B is (7pi)/12 . What is the length of side C?

Aug 9, 2016

$C = 15.4$

#### Explanation:

As per law of cosines
${C}^{2} = {A}^{2} + {B}^{2} - 2 A \times B \times \cos \left(\theta\right)$ where A=7;B=12 and theta=(7pi)/12
or
${C}^{2} = {7}^{2} + {12}^{2} - 2 \times 7 \times 12 \times \cos \left(\frac{7 \pi}{12}\right)$
or
${C}^{2} = 49 + 144 - 168 \times \left(- 0.2588\right)$
or
${C}^{2} = 49 + 144 + 43.48$
or
${C}^{2} = 236.4 .8$
or
$C = \sqrt{236.48}$
or
$C = 15.4$