# A triangle has sides A, B, and C. Sides A and B are of lengths 8 and 1, respectively, and the angle between A and B is pi/12. What is the length of side C?

Mar 2, 2016

≈ 7.039

#### Explanation:

Given 2 sides and the angle between them , as in this question use the $\textcolor{b l u e}{\text{ Cosine rule }}$

For this triangle this is ${C}^{2} = {A}^{2} + {B}^{2} - \left(2 A B \cos \left(\frac{\pi}{12}\right)\right)$

hence:${C}^{2} = {8}^{2} + {1}^{2} - \left(2 \times 8 \times 1 \cos \left(\frac{\pi}{12}\right)\right)$

 = 64 + 1 -( 16 cos(pi/12)) ≈ 49.545

rArr C^2 = 49.545 rArr C = sqrt49.545 ≈ 7.039