BD-BDMO 2015 Problem 5

A tetrahedron is a polyhedron composed of four triangular faces. Faces $ABC$ and $BCD$ of a tetrahedron $ABCD$ meet at an angle of $\pi/6$ . The area of triangle $\triangle ABC$ is $120$ . The area of triangle $\triangle BCD$ is $80$ , and $BC = 10$ . What is the volume of the tetrahedron? We call the volume of a tetrahedron as one-third the area of it's base times it's height.