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

Feb 10, 2016

≈ 3.24

#### Explanation:

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

for this triangle the cosine rule is :

${C}^{2} = {A}^{2} + {B}^{2} - \left(2 A B \cos \left(\frac{\pi}{8}\right)\right)$

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

$= 25 + 4 - \left(20 \cos \left(\frac{\pi}{8}\right)\right) = 29 - \left(18.478\right) = 10.522$

 C^2 = 10.522 rArr C =sqrt10.522 ≈ 3.24