The basic works, the recursion is next

PinwheelTiling/PinwheelTilingPath.cs

@@ -1,4 +1,5 @@
-using LeoTurtle;
+using Avalonia.Controls.Selection;
+using LeoTurtle;
 
 namespace PinwheelTiling;
 
@@ -7,6 +8,8 @@ public static class PinwheelTilingPath
     private const double Alpha = 26.57D;
     private const double Beta = 90D - Alpha;
     private const double Gamma = 90D;
+    private static Point _startPoint = new Point(0, 0.2);
+    private static Point _endPoint = new Point(0, 0);
 
     /// <summary>
     ///     Executes the logic for adding turtle path steps.
@@ -17,10 +20,71 @@ public static class PinwheelTilingPath
     {
         var initialTriangle = new Triangle(new Point(2.5D, 10.0D), new Point(82.5D, 50.0D), new Point(82.5D, 10.0D));
         
-        // TODO - call your drawing/subdivision method
+        const double sideA = 40.0D;
+        const double sideB = 80.0D;
+        double sideC = CalculateHyptonuse(sideA, sideB);
+        MakeTriangle(turtle, sideA, sideB, sideC);
     }
 
     // TODO - implement your algorithm
+    private static void MakeTriangle(SmartTurtle turtle, double sideA, double sideB, double sideC)
+    {
+        double height = CalculateHeight(sideA, sideB, sideC);
+        double sideE = height / 2;
+        double sideF = CalculateHyptonuse(sideE, height);
+        _endPoint = new Point(_startPoint.X + sideB, _startPoint.Y + sideA);
+        
+        //Draw it now
+        DrawTriangle(turtle, sideA, sideB, sideC, height, sideE, sideF);
+
+        double CalculateHeight(double a, double b, double c)
+        {
+            double s = (a + b + c) / 2;
+            return (2 / c) * Math.Sqrt(s * (s - a) * (s - b) * (s - c));
+        }
+    }
+
+    private static void DrawTriangle(SmartTurtle turtle, double a, double b, double c, double h, double e, double f)
+    {
+        //Draw base triangle
+        turtle.Teleport(_startPoint.X, _startPoint.Y);
+        turtle.Turn(90);
+        DrawLine(turtle, b, -Gamma);
+        DrawLine(turtle, a, -(Gamma + Alpha));
+        DrawLine(turtle, c);
+        
+        //Draw the height
+        turtle.Teleport(_endPoint.X, _startPoint.Y);
+        turtle.Turn(-Alpha);
+        DrawLine(turtle, e, -90);
+        double[] halfHeightPosition = turtle.GetPosition();
+        DrawLine(turtle, h);
+        turtle.Teleport(halfHeightPosition[0], halfHeightPosition[1]);
+        turtle.Turn(-Alpha);
+        DrawLine(turtle, e, -(90 + Alpha));
+        DrawLine(turtle, f);
+        
+        //reset angle
+        ResetAngle(turtle);
+        turtle.Turn(-Alpha);
+        DrawLine(turtle, e);
+        
+        void DrawLine(SmartTurtle turtle, double distance, double angle = 0)
+        {
+            turtle.MoveForward(distance);
+            turtle.Turn(angle);
+        }
+
+        void ResetAngle(SmartTurtle turtle)
+        {
+            turtle.Teleport(turtle.GetPosition()[0], turtle.GetPosition()[1]);
+        }
+    }
+    
+    private static double CalculateHyptonuse(double a, double b)
+    {
+        return Math.Sqrt(Math.Pow(a, 2) + Math.Pow(b, 2));
+    }
 
     /// <summary>
     ///     Converts an angel from degrees to radians.