ABCA1B1C1 is a prism which has regular triangles in the bases. The side of the prism has the length "a". The side AA1 makes equal angles with the sides of the base AB and AC, these angles have the value "alfa". We know that AA1 has the length "b". I need to find out the height of the prism.

Question

I figured out that the height of the prism would be h=b*sin(beta), where beta it is the angle formed by AA1 and the base ABC. I don't know how to find out beta.

The final answer should be h=b*sqrt(1-4/3*cos^2(alfa)) .

Thanks in advance (a lot).