1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Finding Coordinates of last Triangle Vertex

  1. Mar 17, 2012 #1
    I am trying to find the last vertex coordinates of a triangle given that

    Vertex 1 = (2,10)
    Vertex 2 = (3,6)

    Angle at Vertex 1 = 75.9638 degrees
    Angle at Vertex 2 = 70.3462 degrees.

    I have tried using the equations based on the length of each side, as well as using the cos dot product rule to try to find x,y but I cannot seem to .

    I always end up with the same equations using both methods, hence only giving me 1 equation for 2 unknowns.
  2. jcsd
  3. Mar 17, 2012 #2


    User Avatar
    Science Advisor

    You can use the sine law. The distance between vertices 1 and 2 is [itex]\sqrt{(2- 3)^2+ (10- 6)^2}[/itex][itex]= \sqrt{1+ 16}= \sqrt{17}[/itex].
    Further, the angles must add to 180 degrees so the angle at vertex 3 is [itex]180- 75.9638- 70.3462= 33.69[/itex] degrees.
    So the length, r1, of the side from vertex 1 to vertex 3, the side opposite vertex 2, is given by [itex]r1/sin(70.3462)= \sqrt{17}/sin(33.69)[/itex]. Write the equation of the circle with center at vertex 1 with that radius.
    And the length, r2, of the side from vertex 2 to vertex 3 the side opposite vertex 1, is given by [itex]r2/sin(75.9638)= \sqrt{17}/sin(33.69)[/itex]. Write the equation of the circle with center at vertex 2 with that radius.

    Find the points where those two circles intersect by solving the equations simultaneously. There are two solutions, one on either side of the line from vertex 1 to vertex 2.
  4. Mar 18, 2012 #3
    Thanks for the reply HallsofIvy,

    I end up with only 2 complex roots for some reason when i use these 2 equations

    (x-3)^2 + (y - 6)^2 = 52 =(r2^2)
    (x-2)^2 + (y-10)^2 = 49 = (r1^2)

    i got 10x^2 - 284x +2652 = 0 after substitution.

    the answer i am suppose to get for the last coordinate is (9,10)
  5. Mar 18, 2012 #4
    oops my mistske, i did some calculation errors.

    hmm is there anyway to pick the right coordinates when i end up with 2 solutions?

    Both will have the same angle between the vectors , so theres no way to tell which is the coordinate im looking for?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook