# A triangle has sides A, B, and C. Sides A and B are of lengths 2 and 5, respectively, and the angle between A and B is (5pi)/8 . What is the length of side C?

Mar 30, 2017

5,73

#### Explanation:

Use the cosine law in this situation. The cosine law states the following for ANY triangle.
${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cdot \cos \left(Y\right)$
With Y= angle between a and b.

So $Y = \frac{5 \cdot \pi}{8}$

If the angle is nice and the cosine gives a value displayed in pi, the senses is much nicer. For this calculation one cannot simplify it.