# A triangle has sides A, B, and C. Sides A and B are of lengths 6 and 9, respectively, and the angle between A and B is pi/6. What is the length of side C?

$c = 4.84451$ units

#### Explanation:

Given two sides and an included angle

$a = 6$, $b = 9$, $C = \frac{\pi}{6}$

Law of Cosine

$c = \sqrt{{a}^{2} + {b}^{2} - 2 \cdot a \cdot b \cdot \cos C}$
$c = \sqrt{{6}^{2} + {9}^{2} - 2 \cdot 6 \cdot 9 \cdot \cos \left(\frac{\pi}{6}\right)}$

$c = \sqrt{23.46925639128}$

$c = 4.84451$

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