How to find the magnitude of a vector when I know the angle it travels from a point to a line?

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I have a point P and straight line L in 2D space. From point P, I can find the vector V reaching perpendicular to the line L.
Suppose I rotated the vector V by θ about point P. Let's say this rotated vector is V'.
If we assume that this rotated vector V' can be extended to reach the line L, how do we find the magnitude of this vector?

I want to know the magnitude of red vector in this image.