Finding Signed Angle Between Three Points

Question

I have seen explanations of how to find the angle defined by three points, A, B and C. However, all the examples I have seen yield absolute angular values. That is to say, the angle value for A->B->C is the same positive value as the value for C->B->A. I am trying to calculate positive or negative angular values, using the right hand rule to determine sign. Any help would be much appreciated.

Answer 1

Note that your solution must be positive because they are all part of a triangle with vertices ABC. If the angles could be negative, then the angles wouldn't add up to $180^o$. Or you would have to have an angle be larger than $180^o$ to make up for the other angles. We can have other angles be negative because they are relative to a ray, usually the x-axis. One direction from this ray is positive, the other is negative. What you are mentioning is a ray, but it changes for your two examples. For $A\to B\to C$, the ray that the angle is relative to is ray $A\to B$, making the angle indeed positive. Working it from the other direction changes the ray and the way you have to view the angle. Hope I answered correctly and fulfillingly and do mind my using of the work ray at the end.