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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!

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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.

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  • $\begingroup$ That's exactly the point i was thinking about, but I thought that I'm missing something and I can add another "constraint" from the given conditions. Thank you for making it clear, have a great day! $\endgroup$
    – J. Newbie
    Sep 26, 2019 at 7:24

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