Because of this relationship, you can solve for one unknown (the actual
size, or diameter, for example) if you know the other two (the angular size
and the distance, in this case). In fact, that is exactly what you are
going to do to find the size of the central star in HT Cas and answer the
challenge question. Once you find or measure HT Cas's angular size and its
distance from Earth, you can plug the values into the equation above and
solve for its actual size.
The 1.5 x 108 is a conversion factor to account for the
units used in this problem, which need to be consistent. Parsecs are
based on parallax, as measured from the Earths orbit which has a
radius of 1.5 x 108 km.
Find the distance from Earth to HT Cas using parallax.
Find the angular size of HT Cas