The bisector of acute angle $\alpha$ of the right triangle $ABC$ splits the side $a$ in two segments with lengths $m$ and $n$. Find the acute angle $\beta$ and the lenths of the other two sides by knowing $m$ and $n$.
Source: Kosovo MO 2012 Grade 11, Problem 2
Tags: geometry
The bisector of acute angle $\alpha$ of the right triangle $ABC$ splits the side $a$ in two segments with lengths $m$ and $n$. Find the acute angle $\beta$ and the lenths of the other two sides by knowing $m$ and $n$.