What evidence do we have that giant stars really are bigger than the sun?

"Giants are more luminous than main sequence stars of the same
temperature.
Therefore they must be larger i.e. giants."

http://phys.strath.ac.uk/12-147/handouts/lecture17.pdf "12.147
Astronomy
Part III Stars, Galaxies, Cosmology" by Gordon Robb (I encourage you
to examine this resource in its entirety for a full background.)

"a star's luminosity increases with mass as (the star's mass)[^]p."

http://www.astronomynotes.com/evolutn/s2.htm# " Stellar Evolution" by
Nick Strobel

Sincerely,

Wonko

Excellent!! Thanks!