Hi bjhopper! Thanks again for your reply

I understand most of your explanation but I didn't understand some parts, where you said to swing arcs and a vertical line.

If you ever wish to make some quick graphs, not only on this thread. There's a tool called CaRMetal that is by java, so you don't have to install anything.

So we can better understand you. Search CaRMetal on Google, it is a French program

What do you mean with many triangles?

And what do you mean with fixing the length?

Here's what I got

$\displaystyle 9=36+x^2-12xcos{(a)}$

$\displaystyle cos{(a)}=\frac{+x^2+25}{12x}$

and

$\displaystyle 16=36+y^2-12ycos{(a)}$

$\displaystyle cos{(a)}=\frac{+y^2+20}{12y}$

If we were to equal those two equations, would we get anywhere?

About the Stewart's Theorem,

the theorem is $\displaystyle a(mn+d^2)=b^2m+c^2n$

But we can't use it here with that few measures.

But I didn't want to do it with it,

The last time I did this question, I didn't get it right. That's why I am asking for it again.

I used a property of right triangles, and we don't know if this is a right triangle (eventually we do, but).

I don't know how you guys got AC=6 with the bisector theorem

If I get something wrong, it is maybe because it is late here and I am kind of tired hahaha

Thanks bjhopper!