$ABC$ and $ADB$ are isosceles triangles. Given $\beta,$ $R$ and $h$, how can I find angle $\alpha$?
$\beta$ is the top angle of the triangle $ABC$, so $\angle{ACB}$.
$h$ is the change in height between $ABC$ and $ADB$.
$R$ is the length of one of the legs of the isosceles triangle $ADC$, so $\vec{|AD|}$ and $\vec{|DC|}$.
$\alpha$ is the top angle of the triangle $ADB$, so $\angle{ADB}$
My friend and I worked on it a bit, but we found some really complicated solution that was unusable. The problem itself seems pretty simple, so I feel like we did a wrong step at one point. Any help appreciated!
Here is an image of the Isosceles Triangles better describing the problem: