If the Sun set below the western horizon three hours ago, and the Moon is barely visible on the eastern horizon, what phase would the Moon be in?

The correct phase of the Moon in this scenario is the Waning Crescent. When the Sun sets in the western horizon, its position indicates it is evening. If the Moon is barely visible on the eastern horizon, it suggests that it has recently risen and is relatively low in the sky.

This positioning aligns with a Waning Crescent phase, which typically occurs in the days following the New Moon. During this phase, the Moon rises shortly before the Sun, leading to its visibility just after sunset and before sunrise. Since the Moon is visible shortly after sunset and appears thin and crescent-shaped, this confirms that it is in the Waning Crescent phase.

In contrast, a New Moon would not be visible at all, as the Moon is located between the Earth and the Sun, and the illuminated side is facing away from us. A Waning Gibbous phase, on the other hand, would have the Moon rising a few hours after sunset, which would not match the described scenario. A Full Moon would be positioned opposite the Sun in the sky, rising at sunset, and thus would not be able to be seen on the eastern horizon shortly after sunset.