θ = 20 microarcseconds = .02 arcsec = 9.7 x 10-8 radians
When you make the approximation A/θ = B you must use the degrees that give you a lower number. So for .1 arcsec the maximum parallax distance is .1 ly.
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No, you need to use radians not degrees.
You need to use the value that give you the lower number when using the approximation.
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1 AU / 0.1 arcsec = 1 AU / 4.85x10-7 radians = 32.6 ly (or calculated using degrees .1 ly).
Does that mean the maximum distance to a star is 33 ly?