AIME 1984 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 $\text{cm}^3$.