Can we measure the original angle of an object in a picture if we know the angle of rotation of said object

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Say we have a triangle with corners A, B and C. Now imagine this triangle in 3d space where it is orthogonal to the z-axis and the center of the triangle is in the origin. We are an observer and we stand some distance from the triangle on the z-axis looking at the thing.

Say the angle is now rotated a few degrees around either the x or y axis, we now see the triangle at an angle. When we now look at the triangle, we perceive three different corners A', B' and C', as from our viewpoint the corners look different now due to the rotation.

Is it possible to calculate the original A, B and C from the perceived corners A', B' and C' knowing the distance we are from the triangle?

I apologize if this description isn't mathmathically sound, I am still a noob