# In triangle ABC, a=6.3. B=9.4, <C=38.3° how do you find side C?

May 10, 2018

The length of side $c$ is approximately 5.9.

#### Explanation:

You use the Law of Cosines - 'cause it's the LAW!

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

Soving for $c$ gives us the equation

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

Here $a = 6.3$, $b = 9.4$, and $\theta = {38.3}^{\circ}$, so

$c = \sqrt{{6.3}^{2} + {9.4}^{2} - 2 \left(6.3\right) \left(9.4\right) \cos {38.3}^{\circ}} \approx 5.9$