WebKit

If you read this in the future here is a more optimized version of the script function drawTriangleWithRightTriangles(x1, y1, x2, y2, x3, y3)
  y1 = -y1
  y2 = -y2
  y3 = -y3

  local t1 = castle.createActor("Right Triangle", 0, 0)
  local t2 = castle.createActor("Right Triangle", 0, 0)
  t1:moveToFront()
  t2:moveToFront()

  local dx12, dy12 = x2 - x1, y2 - y1
  local dx23, dy23 = x3 - x2, y3 - y2
  local dx31, dy31 = x1 - x3, y1 - y3

  local s1 = (dx23^2 + dy23^2)^0.5
  local s2 = (dx31^2 + dy31^2)^0.5
  local s3 = (dx12^2 + dy12^2)^0.5

  local a1 = math.acos((s1^2 + s2^2 - s3^2) / (2 * s1 * s2))
  local a2 = math.acos((s2^2 + s3^2 - s1^2) / (2 * s2 * s3))
  local a3 = math.acos((s3^2 + s1^2 - s2^2) / (2 * s3 * s1))

  local ox, oy, bx, by, ax, ay, side, angle
  if a1 >= a2 and a1 >= a3 then
    ox, oy = x3, y3; bx, by = x1, y1; ax, ay = x2, y2; side = s2; angle = a2
  elseif a2 >= a3 then
    ox, oy = x1, y1; bx, by = x2, y2; ax, ay = x3, y3; side = s3; angle = a3
  else
    ox, 

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Transparent triangle filler It's poorly optimized right now since it's a proof of concept.

Transparent triangle filler It's poorly... - by @Area52 on Castle