# A triangle has sides A, B, and C. Sides A and B are of lengths 10 and 12, respectively, and the angle between A and B is (5pi)/8 . What is the length of side C?

Aug 13, 2016

$C = 18.33$

#### Explanation:

As per law of cosines
${C}^{2} = {A}^{2} + {B}^{2} - 2 A \times B \times \cos \left(\theta\right)$ where A=10;B=12 and theta=(5pi)/8
or
${C}^{2} = {10}^{2} + {12}^{2} - 2 \times 10 \times 12 \times \cos \left(\frac{5 \pi}{8}\right)$
or
${C}^{2} = 100 + 144 - 240 \times \left(- 0.383\right)$
or
${C}^{2} = 100 + 144 + 91.84$
or
${C}^{2} = 335.84$
or
$C = \sqrt{335.84}$
or
$C = 18.33$