# A triangle has sides A, B, and C. Sides A and B are of lengths 7 and 3, respectively, and the angle between A and B is pi/6. What is the length of side C?

May 19, 2016

$C = 9.715$

#### Explanation:

Here we know two sides $A$ and $B$, which are $7$ and $3$ and angle between them, which is $\frac{\pi}{6}$.

To find third side, we can use cosine formula.

Hence ${C}^{2} = {7}^{2} + {3}^{2} - 2 \times 7 \times 3 \times \cos \frac{\pi}{6}$

or ${C}^{2} \equiv 49 + 9 + 42 \times 0.866 = 58 + 36.372 = 94.372$

or $C = \sqrt{94.372} = 9.715$