I have values for x,y,z coordinates of two points A and B as in attached figure, my objective is to determine a third point C hence making a triangle. Since I could determine distance values between the points, I tried to obtain the angles BAC and ABC. However when I used cosine formula, the value I obtained for cosA is not within the range of [-1, 1]. Hence the inverse cosine resulted in Complex number. How can I avoid or deal with such situation? Please I will appreciate any guide Triangle from the two points A,B and Point C to be determined
2026-04-01 17:26:30.1775064390
How to Overcome Complex Number in Inverse Cosine
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Your linked diagram lists the side lengths of your putative triangle to be $$|AB| = 10.8, \quad |AC| = 53.12, \quad BC = 11 $$ Here's the problem: those side lengths contradict the triangle inequality. If $x,y,z$ are the lengths of the three sides of a triangle, then the triangle inequality is $$x \le y + z $$ This is violated for $x=|AC|$, $y=|AB|$, $z=|BC|$. So there does not exist any triangle with those side lengths.