1. 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.

2. Originally Posted by longshorts
...

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.