how do you find the actual diameter of a star going from arcseconds to kilometers?ex The supergiant star Betelgeuse (in the constellation Orion) has a measured angular diameter of 0.044 arcsecond. Its distance has been measured to be 427 light-years. What is the actual diameter of Betelgeuse?

What you have is a skinny, skinny sector of a circle ... like a slice of pie.The radius of the pie is 427 light-years, and the angle in the center, at the tip of the slice, is 0.044 second.  That's about  0.000012 degree.  The question is:  What's the length of the crust out at the fat end of the slice ?This is a case where it's very handy to measure your angles in radians instead of degrees. That way, whatever fraction of a radian is at the tip, the same fraction of the radius is the length of the arc (the crust).To change degrees to radians, multiply by  (pi)/180 .0.044 second = 0.000012 degree = about  2.133 x 10^-7 radian .So the diameter of the star is about  (2.133 x 10^-7) of 427 light years.I'll leave that part for you to finish up.