Good Evening,
I am just starting out in GIS and it's been a long time since I took math in university. I am teaching myself through a textbook but there's a few questions I am stumped on. If anyone can help me solve this one I'll be rolling through them in no time!
Essentially I have a triangle. Say one point is A, the other is B and the third is C. I have the coordinates for point A and B. I have the azimuths from A to C and from B to C. I am trying to find out what the coordinates of point C.
Does anyone have any suggestions? This is very basic, first year (probably even high school level ^_^) trigonometry. Any help is greatly appreciated!
-Li
Assume (as is common in geography) that azimuth is measured from north and increases clockwise. Suppose $A=(x_1,y_1)$ and $B=(x_2,y_2)$ and the azimuths from these two points are $z_1$ and $z_2$ radians espectively.
The line from $A$ with bearing $z_1$ has the equation $$y-y_1=(\cot z_1)(x-x_1)$$ Similarly, the line from $B$ with bearing from $z_2$ has the equation $$y-y_2=(\cot z_2)(x-x_2)$$ $C$ must lie on both these lines, and this is a linear system where the unknowns are $x$ and $y$. Thus solving for those variables will yield the coordinates of $C$.