The red supergiant Betelgeuse has a surface temperature of 3600 K.
a) Using the fact that the Sun's surface temperature is about 5800 K and that its continuous spectrum peaks at a wavelength of 500 nm, find the peak wavelength of Betelgeuse's continuous spectrum. (Please enter your answer in units of nanometers)
b) Betelgeuse has a luminosity that is 120,000 times that of the Sun. Find Betelgeuse's radius. (Please enter your answer in units of kilometers)