height (180/π)x60x60=206264.806... AU which defines the parsec (pc).
Usually one thinks of the Earth sweeping out a baseline of one AU, then the parallax π" of a star referred to a baseline of one AU gives the surveyed distance r(pc)=1/π". (If your baseline is x AU just divide the measured parallax by x. It's linear for such small angles.)
But you can turn this around to obtain the plate scale in AU if you know it in arcsec and you know the distance to the object. For example, those Hubble WideFieldCameraAdvancedCameraforSurveys (WFC ACS) pictures have a 202"x202" field with 0.05" pixels. So if the Great Nebula in Orion (M42) is 460 pc distant then one arcsec is 460 AU, the field is 92920 AU by 92920 AU or about 0.45 pc on a side and each pixel is 23 AU on a side.
Sadly, NASA and most people that post these neat pictures give distances in light years instead of pc so you have to divide the light years by 3.26 to get the distance in pc. So
Scale = (distance in pc) AU per arcsec
One of the first parallax measurement ideas was not using the Earth orbit as a baseline but rather a close visual binary/spctroscopic binary. The visual orbit gives the semimajor axis (arcsec) and orbital inclination i while the spectroscopic measurement gives the size of the orbit (a sin i) in AU. Then
r(pc)=a(AU)/a(").
But in 1838 the actual annual parallax of 61Cyg was measured by Bessel. Only recently has this method come into its own with a combination of high precision spectroscopy for radial velocity measurement and techniques such as speckle interferometry for the physical orbit determination.
Exploding stars can eject shells of matter that can be observed over time to reveal an expansion rate in arcsec per year. If we assume a spherical explosion the radial velocity is easily measured in km/s which, divided by 4.74 gives an expansion rate in au/yr. The ratio of AU/yr to arcsec/yr gives the distance in pc.
Recent observational techniques are revealing stellar disks! Certain pulsating variables (Mira) can be observed to wax and wane both spectroscopically (km/s or 4.74 AU/yr) and physically (arcsec per year) again revealing a distance.