Given a point $A(x, y)$ in a $2$D plane and two perpendicular vectors having their origin in $A$ with their corresponding magnitude (length). Also given that the $2$ vectors are perpendicular, is it possible to find the angle between the $OX$ axis and one of the vectors (if we know one angle, the other is $\pm \frac \pi2$, so it does not matter which one)?
I attached a picture for a better understanding.Scenario description Is it possible to find the $\beta$ angle only knowing A's coordinates $(x, y)$, the length of $L_1$, the length of $L_2, L_1$ and $L_2$ are perpendicular, $L_1$ and $L_2$ segments have their origin in $A$. We do not have any information about the $B$'s or $C$'s coordinates.
Thank you!