I've got the next figure:

Now I would like to calculate the height, so from D to the plane ABC.
First, I've tried with a coordinate system, but it's to difficult to take these distances into account.
Then I remarked that all the faces (the triangulars) are similar. But I don't see if I can use that to calculate the height.
Can someone give me an idea about how to start?
Silke
Put A at (0,0,0}, and B at (0,15,0). Calculate C at (x,y,0). Then solve the intersection of the three sphere equations.