# A triangle has sides A, B, and C. Sides A and B are of lengths 8 and 9, respectively, and the angle between A and B is (5pi)/12 . What is the length of side C?

Dec 16, 2016

#### Answer:

$\left\mid C \right\mid \approx \textcolor{g r e e n}{10.3793}$

#### Explanation:

The Law of Cosines tells us that
$\textcolor{w h i t e}{\text{XXX}} \left\mid C \right\mid = \sqrt{{\left\mid A \right\mid}^{2} + {\left\mid B \right\mid}^{2} - 2 \left\mid A \right\mid \left\mid B \right\mid \cos \left(c\right)}$
where $c$ is the angle opposite side $C$ (i.e. the angle between $A$ and $B$)

$\left\mid C \right\mid = \sqrt{{8}^{2} + {9}^{2} - 2 \cdot 8 \cdot 9 \cdot \cos \left(\frac{5 \pi}{12}\right)}$

using a calculator (or spreadsheet) should (if I haven't messed up) give the answer above.