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September 1st, 2019, 12:10 PM  #1 
Newbie Joined: Aug 2019 From: Denmark Posts: 3 Thanks: 0  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. 
September 1st, 2019, 02:52 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,823 Thanks: 723 
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: $BC^2=AC^2+AB^22ABAC\cos(a).$ I presume angle $a$ is at point $A$. Last edited by skipjack; September 1st, 2019 at 03:08 PM. 
September 1st, 2019, 03:19 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,972 Thanks: 2222 
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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angle, calculate, length, line, point, triangle 
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