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Math Help - Getting the gradient of a line in a triangle

  1. #1
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    Getting the gradient of a line in a triangle

    Hi all, Im a computer scientist at university and urgently need help with working out a geometric problem. Ill try and specify the problem as simply as I can.

    I have a triangle between the points H, E, S. I know the distances between all these points and the all the angles of the triangle. However I only know the (x,y) coordinates of H and S. Ultimately, I am trying to find the coordinates of E.

    In order to do this I am trying to work out the intersection of two y = mx + c lines, HE and SE. I can work out the gradient (m) of HS as I have the coordinates of H and S, but how can I work out the gradient of both HE and SE presumably using the angles that I know in the triangle?

    Also please note, these values are variable, so I cant work this out using a grid of some sort as I have no constant values.

    Thanks in advance for any help.
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  2. #2
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    Quote Originally Posted by longshorts View Post
    ...

    I have a triangle between the points H, E, S. I know the distances between all these points and the all the angles of the triangle. However I only know the (x,y) coordinates of H and S. Ultimately, I am trying to find the coordinates of E.

    In order to do this I am trying to work out the intersection of two y = mx + c lines, HE and SE. I can work out the gradient (m) of HS as I have the coordinates of H and S, but how can I work out the gradient of both HE and SE presumably using the angles that I know in the triangle?

    Also please note, these values are variable, so I cant work this out using a grid of some sort as I have no constant values.

    Thanks in advance for any help.
    Here is a starter to solve the problem:

    The point E is the point of intersection of the two circles around H and S with the sides HE and SE as radii. Since you know the coordinates of H and S the equations of the two circles are:

    (x-x_H)^2+(y-y_H)^2=(\overline{HE})^2

    (x-x_S)^2+(y-y_S)^2=(\overline{SE})^2

    Since two circles (normally) intersect in two points you must construct an algorithm to determine the correct point of intersection.
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