How to find the location of a point in 3D space from projected 2D angle

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I have points $A,B,C$ in 3D space and I know the position of $A=(x_1, y_1, z_1)$ and $B=(x_2, y_2, z_2)$. I want to find the location for $C$ given that $AB$ and $BC$ is perpendicular in 3D space but on a 2D plane it's $63.8^{\circ}$

Is it possible to find the location of $C$ with the provided information above?

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Projection of points onto image plane