Estimate the diameter of the supergiant star betelgeuse, using its angular diameter of about 0.05 arcsecond and distance of about 600 light-years.

To answer this problem, we use the equation,

physical size = (2π) (distance) (angular size) / 360°

We have to convert first the given angular size of 0.05 arcsecond to degrees by following the steps below,

(0.05 arcsecond) (1 arcminute/60arcsecond) (1°/60 arcminute) = 1.39 x 10^-5°

Using the equation above,

physical size = (2π) (600 light years) (1.39 x 10^-5°) / 360°

= 1.45 x 10^-4 light years