
Imagine the setup above; how can I calculate the points P1 and P2 if all angles, all sides A,B,C and point P3 are known?

Imagine the setup above; how can I calculate the points P1 and P2 if all angles, all sides A,B,C and point P3 are known?
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If by ''sides'' you mean the length of the sides: it's not possible. Imagine a triangle made out of cardboard (all sides/angles fixed) that's fixated with a nail on one end point. You can still rotate the triangle and thereby move the position of the other two endpoints.
If you mean the vectors that make up the sides, you can calculate the missing points by adding the corresponding vectors to the given point.