Answer
$3960mi$
Work Step by Step
Step 1. Identify the quantities: angle $\theta=60.276^\circ$, height of satellite $h=600mi$, radius of the Earth $R$
Step 2. In the right triangle given in the figure of the problem, the hypotenuse is $R+h$, and $sin\theta=\frac{R}{R+h}$, so that $R=(R+600)sin60.276^\circ$ which gives $(1-sin60.276^\circ)R=600sin60.276^\circ$ and
$R=\frac{600sin60.276^\circ}{1-sin60.276^\circ}\approx3960mi$
