1992 AIME Problem 7

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.