# A triangle has sides A, B, and C. Sides A and B are of lengths 1 and 8, respectively, and the angle between A and B is (5pi)/8 . What is the length of side C?

Feb 13, 2016

C ≈ 8.43

#### Explanation:

In this triangle , 2 sides and the angle between them are known , hence use the$\textcolor{b l u e}{\text{ cosine rule }}$

${C}^{2} = {A}^{2} + {B}^{2} - \left(2 A B \cos \theta\right)$

here A = 1 , B = 8 and $\theta = \frac{5 \pi}{8}$
substitute these values into the formula

${C}^{2} = {1}^{2} + {8}^{2} - \left(2 \times 1 \times 8 \cos \left(\frac{5 \pi}{8}\right)\right)$

= 1 + 64 - ( -6.12) = 65 + 6.12 = 71.12

C^2 = 71.12 rArr C =sqrt(71.12) ≈ 8.43