# 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 (7pi)/8 . What is the length of side C?

Dec 19, 2016

c=5.8737

#### Explanation:

The figure explaining the given data is given below:

To find side 'c', Cosine rule would apply in this case. Cosine rule says that

Cos C= $\frac{{a}^{2} + {b}^{2} - {c}^{2}}{2 a b}$. Plugging in the given values, it would be

$C o s \left(\frac{7 \pi}{8}\right) = \frac{4 + 16 - {c}^{2}}{16}$

${c}^{2} = 20 - 16 \cos \left(\frac{7 \pi}{8}\right) = 20 - 16 \cos \left(\pi - \frac{\pi}{8}\right) = 20 + 16 \cos \left(\frac{\pi}{8}\right) = 20 + 14.5009 = 34.5009$

c=5.8737