I know there's some math/geometry guru's out there, and I need your help. I need to find in 3d space, the co-ords of a third point in a triangle. The length of all three sides are known, and two of the points are known. I googled and there's a slew of information on triangle geometry/math and my head is spinning from the Pythagorean theorem to Heron's formula.

I know in my gut there's a way to find out that tricky 3rd point with so much known. The whole trick here is that the length of one side is dynamic, and therefore the co-ords of the point across from that side would be dynamic as well.

Wait, if the triangle is in 3D space, there's an infinite number of points as you rotate the triangle. You need some kind of vector to know for sure.

I think.

eww, good point. Let's just say I have some vectors?

I know the vector between the two known points is defined. But then, there's still that infinite thing going on... It'd actually be nice to have a couple hundred points to choose from come to think of it.....

Please list everything you know. Exactly.

*giggles*

There was the big bang, then some planets formed, life sprung up on this one.....

(attached a picture to better illustrate)

Anyway, I do not have exact co-ordinates because, well, everythings moving and will have different co-ordinates at any given time. However, if you must:

The length between the two points that are known (Yellow/Red/Orange) can vary, because of the varying 3rd (purple) point. The green side has a length of 0.028096 and the blue side has a length of 0.03375.

Based on that, it'd be easier to think of the yellow (or orange) and pink being fixed, with the other being the variable. That secures one leg, and leaves the other leg free to move. Even then you still have an infinite number of points for that third point to be located at.

If you know the position of two points, and their distance to the third point in 3D space, then the possible answers would form a circle about the line.

Unless you have a vector for at least one of the sides.