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September 1st, 2019, 12:10 PM   #1
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Calculate third point of triangle given angle and line length

I have a triangle with the three points named A, B and C. I know the coordinates of A and B and need to calculate C. I also know the angle a and that |AB|=|AC|. Unfortunately the only formulas for triangles I remember, are about calculating an unknown length or angle, and I need the coordinates for C.

I describe it as a triangle because it can be considered as such, but it is in reality also about a circle with its center in A, and both B and C are on the circumference of the circle, where C is a degrees from B, and |AB|=|AC|=r.
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September 1st, 2019, 02:52 PM   #2
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You can use the law of cosines to get the length of |BC|. You should then be able to get the coordinates of C.

Cosine law: $|BC|^2=|AC|^2+|AB|^2-2|AB||AC|\cos(a).$ I presume angle $a$ is at point $A$.

Last edited by skipjack; September 1st, 2019 at 03:08 PM.
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September 1st, 2019, 03:19 PM   #3
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I'm curious about the wording "in reality". Is this a "real world" problem? If it is, why not use polar coordinates?
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