# A triangle has sides A, B, and C. Sides A and B are of lengths 7 and 1, respectively, and the angle between A and B is (5pi)/12 . What is the length of side C?

side $c = 6.81003$

#### Explanation:

From the given triangle
side $a = 7$ and side $b = 1$
Angle $C = \frac{5 \pi}{12}$

We can solve this using Law of Cosines for sides

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

$c = \sqrt{{7}^{2} + {1}^{2} - 2 \cdot \left(7\right) \cdot \left(1\right) \cdot \cos \left(\frac{5 \pi}{12}\right)}$

$c = \sqrt{49 + 1 - 14 \cdot \cos \left(\frac{5 \pi}{12}\right)}$

$c = \sqrt{50 - 14 \cdot 0.25881904510247}$

$c = 6.81003$

God bless...I hope the explanation is useful.