How to find distance from point to axis at specific angle

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I want to find the distance between a point and an x or y axis, but at a certain angle. Hopefully the diagram below will be able to better explain what I am looking for.

I am trying to find the distance of the red and blue lines, the distance between point $p$ and the x-axis, and point $p$ and y-axis respectfully.

The lines originate from an arbitrary point $p$ and are angled by an arbitrary angle $\theta$ and $\theta+90^\circ$

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This is not difficult, the distance to axis $y$ will be $\large{\frac{|x|}{\sin \theta}}$, the distance to axis $x$ will be $\large{\frac{|y|}{\sin \theta}}$. Just draw lines parallel to axes and consider right triangles that will be formed by constructed lines, axes and your red and blue lines.