# A triangle has sides A, B, and C. Sides A and B are of lengths 9 and 5, respectively, and the angle between A and B is (5pi)/12 . What is the length of side C?

Feb 10, 2016

≈ 9.1

#### Explanation:

In this triangle , 2 sides and the angle between them are known , so use the ' cosine rule"

For this triangle the cosine rule is ;

${C}^{2} = {A}^{2} + {B}^{2} - \left(2 A B \cos \left(\frac{5 \pi}{12}\right)\right)$

$= {9}^{2} + {5}^{2} - \left(2 \times 9 \times 5 \times 0.2588\right)$

= 81 + 25 - 23.3 = 106 - 23.3 = 82.7

now  C^2 = 82.7 rArr C = sqrt82.7 ≈ 9.1