Aperson on earth is observing the moon which is
238,860
miles away. the moon is a diameter of
2160
miles. what is the angle in degrees spanned by the moon's image in the eye of the beholder?

As the moon's diameter is straight, the distance from the observer to the moon and the diameter are at 90°, subtending an angle at the viewer's eye. This is:
tan∅ = diameter / distance
tan∅ = 2160 / 238,860
∅ = 0.52°