Answer
The diameter of the moon is approximately 2156 miles.
Work Step by Step
We can convert the angle to radians:
$\theta = (0.5170^{\circ})(\frac{\pi~rad}{180^{\circ}}) = 0.009023~rad$
Since the diameter of the moon is approximately equal to the arc length, we can estimate the diameter $d$ of the moon:
$d \approx \theta ~r$
$d \approx (0.009023~rad)(238,900~mi)$
$d \approx 2156~mi$
The diameter of the moon is approximately 2156 miles.