Suppose a square of side length $12$. The square has vertices at coordinates $(0,0), (12,0), (0,12), (12,12)$. Inside the square is a point $a$ with all angles known (from point $a$ to any two vertices). You have to find the coordinates of the point.
You tried to solve this by writing a non-linear set of equations using law of cosines.
Where $x,y,z,w$ are distances from point $a$ to the vertices and $\alpha,\beta,\gamma,\delta$ are the angles between point $a$ and two vertices.
You try to solve this numerically but find out that the matrix is singular. Sometimes you get a good approximation, but sometimes the approximation is just wrong. Depends a lot on the initial guess.
You think of another way to solve this, or you resign.