This was a task I had to complete to attempt to find a right angle from 3 cartesian coordinates, +/- 5 degrees. ​

Of course the first place I looked was StackOverflow which led me to this explanation with some ruby code:

def angle_between_points(p0, p1, p2)
  a = (p1[0]-p0[0])**2 + (p1[1]-p0[1])**2
  b = (p1[0]-p2[0])**2 + (p1[1]-p2[1])**2
  c = (p2[0]-p0[0])**2 + (p2[1]-p0[1])**2
  Math.acos( (a+b-c) / Math.sqrt(4*a*b) ) * 180/Math::PI
end

For my purposes, I simply created the three arrays and passed them to the method after a call to puts:

p0 = [2005000,992453]
p1 = [1895297,949433]
p2 = [1920079,884362]

puts angle_between_points p0, p1, p2

Now, I can adjust the numbers in the .rb file and call it at the command line:

chris@IO  ~/Documents/code
$ ruby angle_between_points.rb
90.56350243137959