# Calculate third point of triangle given angle and line length

#### ThemePark

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.

#### mathman

Forum Staff
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 a moderator:

#### skipjack

Forum Staff
I'm curious about the wording "in reality". Is this a "real world" problem? If it is, why not use polar coordinates?