Star a has a parallax angle of 0.02 arcseconds, and star b has a parallax of angle of 0.1 arcseconds. which star is more distant and how much more distant is it?

Star a is more distant and is approximately 5 times as far away as star b Parallax is the change in angle that one must do in order to observe the same object from different locations. The further away an object is, the smaller the parallax is. As the angles approach zero, the trig functions tend to be fairly linear. And 0.1 arc seconds and 0.02 arc seconds are close enough to zero for this to hold true. Since the parallax for star a is smaller than the parallax for star b, it is the more distant star. And since 0.1 divided by 0.02 = 5, it is approximately 5 times further away than star b.

Iwould say a is accurate