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From what I learn, triangulation is a concept where--layman's term-wise--I can find the location of Point of Interest by measuring the distance between Point of Interest and known place of {A, B, C}. In layman's term, if can draw three circle with each circle's center point is one of the position of {A, B, C} and the radius is its distance to Point of Interest, the spot where the three circle coincides is where the Point of Interest located.

The current problem I'm facing with my dataset is I have the distance between A-Point of Interest, B-Point of Interst, and C-Point of Interest, but I am not told where is A, B, C, and Point of Interest. I'm wondering if it's possible to reconstruct where are A, B, and C. The good thing is I have thousands of different Point of Interests and for each Point of Interest I know their distance to A, B, and C.

Realdeo
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You can define the positions of $A,B,C$ and all your points of interest in a particular coordinate frame. For example, you could define that $A$ is the origin and $B$ is on the positive $x$ axis. From there you can locate all the points. You have no information that locates the origin, so you can translate and rotate all the points any way you want. The measured data will not change because none of the distances do.

Ross Millikan
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