Triangle question

mohammad.ashtari · #1 $Old$ June 24th, 2009, 08:34 AM

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

Soroban · #2 $Old$ June 24th, 2009, 09:42 AM

Hello, mohammad.ashtari!

Quote:

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 $AB.$

mohammad.ashtari · #3 $Old$ June 24th, 2009, 09:45 AM

Hi Soroban,

Thanks for your reply. Would you please show me one of the solutions?

Mohammad

Soroban · #4 $Old$ June 24th, 2009, 11:42 AM

Hello, mohammad.ashtari!

Quote:

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.

mohammad.ashtari · #5 $Old$ June 24th, 2009, 12:03 PM

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,

Mohammad

aryanharkawat · #6 $Old$ June 27th, 2009, 03:50 AM

[quote=mohammad.ashtari;332920]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 ?

my friend first u should tell me what r th angles then we can do something ..........

thnks in advance