astrophysics - Distance of a planet to the star?

3 parsecs is the distance from us (Earth, Sun etc) to the star.

At a distance of 1 parsec, the apparent movement of a star wrt the background, as the Earth orbits on its 1 AU orbit is 1 arc second.
So, from 1 parsec distant, the earth would move by 1 arcsec each 6 months. It woukd have an apparevt angular radiusof 0.5 arc sec.

Now this star is 3 parsecs distant, so an orbit with radius 1au would appear to have a angular radius 3 times smaller (here I am approximating, it is valid because the angle is small) or 1/6 arc sec. The planet in the question has a smaller orbit, 6/10 of the Earth, or 0.6 au

The convenient units, and tge the small angles mean that we can avoid trionometry in the solution.