# A triangle has sides A, B, and C. Sides A and B are of lengths 9 and 2, respectively, and the angle between A and B is pi/6. What is the length of side C?

Jun 21, 2018

The length of side C is $7.34$ unit.

#### Explanation:

Angle between Sides $A \mathmr{and} B$ is $\angle c = \frac{\pi}{6} = \frac{180}{6} = {30}^{0}$

Sides $A = 9 , B = 2$ Cosine rule: (for all triangles) is

C^2=A^2 + B^2 − 2 A B cos(c)

:. C^2=9^2 + 2^2 − 2*9*2*cos(30) or

${C}^{2} \approx 53.82 \therefore C \approx 7.34 \left(2 \mathrm{dp}\right)$

The length of side C is $7.34$ unit [Ans]