It may seem obvious in retrospect… but have you noticed that the full moon rises exactly at sunset and sets exactly at sunrise? During a full moon, the moon is positioned directly opposite the sun relative to Earth. As a result, when the sun goes down on the western horizon, the full moon appears on the opposite horizon.
When you see an especially big moon and you’re wondering “is it full tonight?” you can answer that question by figuring out if it rose more or less exactly at sunset. Or you can check this calendar I suppose. 🙂