How long is a lunar day, which is defined by the cycle of the moon's position?

A lunar day, which is determined by the moon's rotation on its axis and its orbit around the Earth, lasts approximately 29.5 Earth days, but when considering the cycle of the moon's position relative to the Earth and the sun, it takes about 24 hours and 50 minutes for the moon to return to the same position in the sky as observed from Earth. This is because while the Moon is completing one rotation on its axis (which takes approximately 27.3 days), it is also moving along its orbit around Earth. Consequently, after completing one rotation, it must rotate an additional amount to catch up with Earth due to Earth's own rotation. This results in a lunar day lasting approximately 24 hours and 50 minutes, making this the correct answer.