# The angle between a segment and the OX axis given segment origin, length and a perpendicular segment

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!

You do not have enough information. take a sheet of paper, put it on a table such that one corner $$A$$ is fixed, and the paper can rotate around $$A$$. Can you tell me what the angle is between the paper and the edge of the table? I have $$A$$, $$L_1$$ and $$L_2$$, and those are perpendicular, but the angle can take any value since I can rotate the paper.