# A triangle has sides A, B, and C. Sides A and B are of lengths 2 and 4, respectively, and the angle between A and B is (11pi)/12 . What is the length of side C?

Side $c = 5.95439 \text{ " }$units

#### Explanation:

The given are 2 sides and an included angle. So, use Law of Cosines for sides

Given $a = 2$ and $b = 4$ and $C = \frac{11 \pi}{12}$

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

c=sqrt(2^2+4^2-2*2*4*cos ((11pi)/12)

c=sqrt(4+16-16*cos ((11pi)/12)

$c = \sqrt{35.45481322}$

$c = 5.95439$

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