1. ## Triangle question

Hi all,

I have a triangle in 3d space which I know the coordinates for two of its vertices A(1,2,3) and B(-1,-2,-3). I also know all the angles of the triangle and all the AB, AC and BC lengths. How can I find the x, y and z coordinates for the last vertex C?

Thanks

I have a triangle in 3-space.
I know the coordinates for two of its vertices $A(1,2,3)$ and $B(-1,-2,-3).$
I also know all the angles of the triangle and all the $AB, AC$ and $BC$ lengths.

How can I find the $x, y$ and $z$ coordinates for the last vertex $C$?
There is an infinite number of solutions . . .

With the given information, you can locate a vertex $C.$
Code:
            C
*
*  *
*     *
*        *
*           *
*              *
--*--*--*--*--*--*--*--
A                 B

But the triangle can be revolved about the side $AB.$

3. Hi Soroban,

Would you please show me one of the solutions?
It's a very messy problem, but I can start it for you.
But you must provide me with some constants.
. . The lengths of $AC$ and $BC$ would be useful.

5. Hi,

I have the answer but I want to find to a general solution to apply for other problems that I do not have their answers. You can use any arbitrary angle and length you want.

Thanks,