Finding the xyz Coordinates of Point C in an Isosceles Triangle

[Sikz]

Finding xyz coords of...

Given: ABC is an isosceles triangle; AB=BC; A(x,y,z); B(x',y',z'); m<ABC=m

I need, based on this information, a way to get the xyz coordinates of C. It's for a computer program I'm writing, and I'm afraid I'm rather unknowlegable about how to solve this type of problem- could someone please give me (an) equation(s) for this? The way those equation(s) work would be appreciated as well, but the equation(s) by themselves are all I really NEED.

Thank you very much.

 

[Integral]

Unfortunately, given that you have expressed this in 3d space you will not be able to find a unique point which completes your triangle. There will be infinitely many triangles, each laying in a different plane.

I am not sure what your constriction
m<ABC=m

means, could you elaborate on that?

 

[Sikz]

Ah yes, such a silly mistake. I assumed I would need xyz coords since the program deals with 3d space, but the triangle is on a plane... I actually only require xy coords.

And by m<ABC=m I meant "measure of angle ABC = m". Since I am unaware of the way to type a proper angle symbol, I used < :P.

 

[Hurkyl]

Well, if angle B has measure m, then the other two angles have measure 90-m/2. Does that help?

(Also, B must lie on the perpendicular bisector of AC)