# Question #4a994

A right triangle with the smallest angle of 22.5º ($\frac{\pi}{8}$ rad) will have the other equal to 67.5º ($3 \frac{\pi}{8}$ rad ). The proportions are fixed:
For a catete with length $a$ will we have the other catete:
$b = a \tan \left(\frac{\pi}{8}\right) = a \left(\sqrt{2} - 1\right)$
$\left(\sqrt{2} - 1\right) = \frac{a}{b}$
Since $\left(\sqrt{2} - 1\right)$ is an irrational number it cannot be found by the ratio between two integer numbers, so the problem doesn't have solution