Given a polygon with 4 unequal sides, consisting of points A,B,C,D, and line segments AB, AC, BD, and DC.
Point A is on the origin. Lengths of AB, AC, BD, and DC are known.
Given a desired coordinate for point D, what would the angle from segment AB to the x axis need to be, and what would the angle from segment AC to the x axis need to be?
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why don’t you give us the lengths of AB, AC, BD, and DC, if they are known?
draw circles with radius AB and center A, radius BD and center D. B will lie at one of the two points at which these circles intersect.
draw circles with radius AC and center A, radius CD and center D. C will lie at one of the two points at which these circles intersect.
this gives you the four possible quadrilaterals for your data.
B and C can be located by equating the circle equations, and then the angle from AB to the x-axis is tan^-1(by/bx) where B = (bx,by)