To solve this problem, we can use the formula for calculating distance using apparent magnitude:
m - M = 5 * log(d/10)
where m is the apparent magnitude, M is the absolute magnitude (which we will assume to be 4.4 for a G2 star), and d is the distance in parsecs.
First, let's convert the apparent magnitude to flux using the zero point flux of -21.10:
f = 10^((m - M + 21.10)/-2.5)
f = 135.86 x 10^-11 erg/cm^2/s
Next, we can use Wien's Law to find the surface temperature of Rigil Kent:
λ_max = 2.898 x 10^-3 m K / T
where λ_max is the wavelength of maximum emission and T is the temperature in Kelvin.
λ_max = 0.5 microns
T = 2.898 x 10^-3 m K / 0.5 x 10^-6 m = 5796 K
This is close to the measured temperature of 5,800 K, so we can assume it is correct.
Now we can use the flux to calculate the luminosity of the star:
L = 4πd^2f
L = 2.107 x 10^33 erg/s
Using the relationship between luminosity, temperature, and radius for main sequence stars, we can find the radius of Rigil Kent:
R = (L/Lsun)^(1/2) (T/Tsun)^(-2)
where Lsun and Tsun are the luminosity and temperature of the Sun, respectively.
R = (2.107 x 10^33 / 3.828 x 10^33)^(1/2) (5796/5778)^(-2) Rsun
R = 0.974 Rsun
Finally, we can use the parallax method to find the distance to Rigil Kent:
π = 1/d
where π is the parallax angle in arcseconds.
π = 0.76 arcseconds (from observations)
d = 1.31 parsecs
So Rigil Kent is about 4.27 light years away from the Earth.