Sorry for coming up with a "do-it-for-me"-question, but I can't think of another way to get help with manually solving the following system of four equations:
$x$, $y$, $\beta$ and $\gamma$ are unknown.
$\alpha$ is a known constant with the given value of $63.5°$.
I tried all approaches I could think of and always got stuck on one equation with two unknown angels, for example $50\tan\beta*(\sin\alpha\tan\gamma+\cos\alpha) = 45\tan\gamma*(\cos\alpha\tan\beta-\sin\alpha)$.
EDIT: This is the numerical solution of WolframAlpha, but, as stated above, I need to do it manually.