# A triangle has sides A, B, and C. Sides A and B are of lengths 4 and 3, respectively, and the angle between A and B is (5pi)/6 . What is the length of side C?

Feb 10, 2016

≈ 2.05

#### 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 :

${C}^{2} = {A}^{2} + {B}^{2} - \left(2 A B \cos \left(\frac{5 \pi}{6}\right)\right)$

hence ${C}^{2} = {4}^{2} + {3}^{2} - \left(2 \times 4 \times 3 \times \cos \left(\frac{5 \pi}{6}\right)\right)$

${C}^{2} = 16 + 9 - \left(24 \cos \left(\frac{5 \pi}{6}\right)\right)$

= 25 - 20.78 = 4.22

now  C^2 = 4.22 rArr C = sqrt4.22 ≈ 2.05