# A triangle has sides A, B, and C. Sides A and B are of lengths 4 and 2, respectively, and the angle between A and B is (5pi)/6 . What is the length of side C?

May 11, 2018

The length of side $C$ is $5.82$ unit.

#### Explanation:

Angle between Sides $A \mathmr{and} B$ is $\angle c = \frac{5 \pi}{6}$

$= \frac{5 \cdot 180}{6} = {150}^{0}$

Sides A=4 , B=2 , C = ?  Cosine rule: (for all triangles)

C^2= A^2 + B^2 − 2 A B cos c

:. C^2=4^2 + 2^2 − 2*4*2*cos150 or

${C}^{2} \approx 33.86 \therefore C \approx 5.82 \left(2 \mathrm{dp}\right)$

The length of side $C$ is $5.82$ unit [Ans]