# Right angled triangle with hyp length 7 contains the angle pi/3. What is exact lengths of the other two sides?

Nov 20, 2015

The other two sides have lengths $\frac{7}{2}$ and $\frac{7 \sqrt{3}}{2}$

#### Explanation:

See image below:
The specified values are in $\textcolor{b l a c k}{\text{black}}$

The standard length ratios of the sides of a $\frac{\pi}{3}$ triangle are in $\textcolor{b l u e}{\text{blue}}$

As can be seen from the hypotenuse the ratio $\left(\text{specified length")/("standard length}\right) = \frac{7}{2}$

So the two non-specified sides have lengths

$\textcolor{w h i t e}{\text{XXX}} \frac{7}{2} \times \textcolor{b l u e}{1} = \frac{7}{2}$
and
$\textcolor{w h i t e}{\text{XXX}} \frac{7}{2} \times \textcolor{b l u e}{\sqrt{3}} = \frac{7 \sqrt{3}}{2}$