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

Feb 14, 2017

Length of side $C$ is $4.36 \left(2 \mathrm{dp}\right)$ unit.
Sides $A = 5 , B = 3$ and angle $\angle c = \frac{\pi}{3} = \frac{180}{3} = {60}^{0}$. Applying cosine law we can find $C = \sqrt{{A}^{2} + {B}^{2} - 2 \cdot A \cdot B \cdot \cos c}$
or $C = \sqrt{{5}^{2} + {3}^{2} - 2 \cdot A \cdot B \cdot \cos 60} = \sqrt{25 + 9 - \cancel{2} \cdot 5 \cdot 3 \cdot \frac{1}{\cancel{2}}} = \sqrt{19} = 4.36 \left(2 \mathrm{dp}\right)$ unit.
Length of side $C$ is $4.36 \left(2 \mathrm{dp}\right)$ unit. [Ans]