I have an irregular tetrahedron as shown in figure below, and I know the length of all of its edges. I want to find the azimuth and zenith angles $\phi$, and $\theta$ for vector $C$.
I managed to find the zenith angle $\theta$ by finding the volume using Cayley-Menger Determinant and the equation volume = $(A\times B).C$; however I can't find the azimuth angle $\theta$.
Any help is appreciated to find azimuth angle $\phi$.
Best regards,
Call $x$ the axis containing the edge $OA$, $z$ the axis wrt the polar angle $\theta$ is measured, $y$ the remaining axis and $\bf c$ the vector $OC$. Knowing the edges, by the cosines rule you can determine the angle $AOC$.
So you have $c_z, c_x$ and can subsequently determine $c_y$ from the $\left\| {\bf c} \right\|$.