# A triangle has sides A, B, and C. Sides A and B are of lengths 7 and 4, respectively, and the angle between A and B is pi/3. What is the length of side C?

Nov 7, 2016

$\left\mid C \right\mid \approx 6.083$ sq.units

#### Explanation:

Consider the image below:

Remember that
$\textcolor{w h i t e}{\text{XXX")sin(pi/3)=sqrt(3)/2color(white)("XX")andcolor(white)("XX}} \cos \left(\frac{\pi}{3}\right) = \frac{1}{2}$

Based on this we have:
$\textcolor{w h i t e}{\text{XXX}} h = 7 \sin \left(\frac{\pi}{3}\right) \approx 6.0621778265$

$\textcolor{w h i t e}{\text{XXX}} x = 7 \cos \left(\frac{\pi}{3}\right) = 3.5$

$\textcolor{w h i t e}{\text{XXX}} k = 4 - x = 0.5$

$\textcolor{w h i t e}{\text{XXX}} \left\mid C \right\mid = \sqrt{{h}^{2} + {k}^{2}} \approx 6.0827625303$