# A triangle has sides A, B, and C. Sides A and B are of lengths 1 and 3, respectively, and the angle between A and B is (5pi)/6 . What is the length of side C?

Mar 29, 2018

c=3.66

#### Explanation:

$\cos \left(C\right) = \frac{{a}^{2} + {b}^{2} - {c}^{2}}{2 a b}$
or
$c = \sqrt{{a}^{2} + {b}^{2} - 2 a b \cos \left(C\right)}$

We know that the sides a and b are 1 and 3
We know the angle between them Angle C is $\frac{5 \pi}{6}$

$c = \sqrt{{\left(1\right)}^{2} + {\left(3\right)}^{2} - 2 \left(1\right) \left(3\right) \cos \left(\frac{5 \pi}{6}\right)}$

c=sqrt((1+9-6(sqrt3/2)

c=sqrt((10-3sqrt3/2)

Enter into a calculator

$c = 3.66$