If the moon is setting at noon, then the sun as at its highest point in the sky when the moon is at the western horizon. This means that the angle between the sun and the moon is 90 degrees. Since the moon moves around the earth from west to east, in about one week, the moon and the sun will be in roughly the same position in the sky. This will be a new moon. One week before the new moon, the moon is at its third quarter half moon phase. Therefore, the phase of the moon must be the third quarter half moon.
