# A triangle has sides A, B, and C. Sides A and B are of lengths 10 and 12, respectively, and the angle between A and B is (7pi)/12 . What is the length of side C?

May 3, 2016

c= 13.4846

#### Explanation:

The question to be solved is as shown in the figure

Now using cosine formula side ${c}^{2} = 100 + 144 - 2 \left(10\right) \left(12\right) \cos \frac{7 \pi}{12}$

${c}^{2} = 244 - 240 \cos {105}^{o}$

$$    = 244-240(-0.2588)  =181.88


c=13.4846