Faces \(ABC^{}_{}\) and \(BCD^{}_{}\) of tetrahedron \(ABCD^{}_{}\) meet at an angle of \(30^\circ\). The area of face \(ABC^{}_{}\) is \(120^{}_{}\), the area of face \(BCD^{}_{}\) is \(80^{}_{}\), and \(BC=10^{}_{}\). Find the volume of the tetrahedron.

(第一十届AIME1992 第7题)