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Homework Help: Trigonometry question, Finding coordinates of 3rd point

  1. Aug 27, 2009 #1
    Heres the situation, I have a triangle in which i found all 3 interior angles. I also have the length of all the sides and the coordinates of 2 points. I just need to find the coordinates of the 3rd point im missing. Is there some formula i need to use for this?
  2. jcsd
  3. Aug 27, 2009 #2


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    Homework Helper

    Sketch the triangle on the xy-axes. Call your points ABC, with B being the unknown. Then find the equation of the line AC and line BC.

    Take the line AC and extend until it cuts the x-axis, find the angle θ between AC and the positive x-axis (so you are measuring the angle to the line counter-clockwise). tanθ will give you the gradient of AC.

    Repeat for BC.

    Solve your two equations and you'll get the coordinates of B!
  4. Aug 28, 2009 #3
    An alternative:

    Let A and C be known. Objective: find coordinates of B.

    (1) Find the slope of the line AC. Call it m.
    (2) Let t = arctan(m). (t may be negative and that's ok)
    (3) Add the angle measure for A to t to get the gradient to B. Call the sum u.
    (4) Find x1 = (AB)cos(u) and y1 = (AB)sin(u) and add these to the coordinates of A respectively to find the coordinates of B.

    I believe this works.


    EDIT: A should be to the left of C (x-axis-wise).
    Last edited: Aug 28, 2009
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