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Sebtimos

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let ABCD be the 4 vertices of the tetrahedron in 3D, all vertices have different (x,y,z).

the coordinate of vertex D is known (Xd,Yd,Zd), and the 3 angle between faces at vertex D are also known angle adb , adc, cdb.

Coordinate of the other 3 vertices A, B, C are known on X, Y but not on Z. (ie Za,Zb,Zc are unknown).

As I can expect this system will give me 2 solutions +&-.

I've started by developing system of equation for the sides using cosines and as a function of Za,Zb,Zc, where (Zb-Za)^2= [Lda^2+Ldb^2-2Lda*Ldb*cos(adb)]-[(xb-xa)^2+(Yb-Ya)^2]

Any suggestions on how to approach this problem would be appreciated.