Target angle submarine observer estimating target angle pictures himself on the target ship looking back at the submarine. Relative bearing of the submarine is the clockwise angle in degrees from the heading of the target ship to a straight line drawn from the target ship to the submarine. When target angle is 0° (or 360° ) the target ship is coming directly toward the submarine. Target angles between 0° and 90° indicate the target ship is moving toward and to the right of the submarine. Target angles between 90° and 180° indicate the target ship is moving to the right and away
Angle trisection and the mark on the line is labeled . This ensures that . A radius is drawn to make it obvious that line segments , , and all have equal length. Now, triangles and are isosceles, thus (by Fact 3 above) each has two equal angles. Hypothesis: Given is a straight line, and , , and all have equal length, Conclusion: angle . Proof: Clearing, , or , and the theorem is proved. Again, this construction stepped outside the framework of allowed constructions by using a marked straightedge. Thomas Hutcheson published an article in the Mathematics Teacher that used a