# A triangle has sides A, B, and C. Sides A and B are of lengths 14 and 9, respectively, and the angle between A and B is (5pi)/12 . What is the length of side C?

Feb 3, 2018

The length of side C is $14.55$unit

#### Explanation:

Angle between Sides $A \mathmr{and} B$ is

$\angle c = \frac{5 \pi}{12} = \frac{5 \cdot 180}{12} = {75}^{0}$ Sides $A = 14 , B = 9$

Cosine rule: (for all triangles) A^2 + B^2 − 2AB cos(c) = C^2

:. C^2=14^2 + 9^2 − 2*14*9*cos(75) or

${C}^{2} \approx 211.78 \therefore C \approx 14.55 \left(2 \mathrm{dp}\right)$

The length of side C is $14.55$ unit [Ans]