1984 AIME Problem 9

In tetrahedron ABCD, edge AB has length 3 cm. The area of face ABC is 15\text{cm}^2 and the area of face ABD is 12 \text{ cm}^2. These two faces meet each other at a 30^\circ angle. Find the volume of the tetrahedron in \text{cm}^3.

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.