Advanced Geometry and The Right Triangle

Properties of triangles (SOH-CAH-TOA and the Pythagorean Theorem).

Industrial applications of trigonometry, such as verifying angles using Sine Bars.

The geometry of Tapers and how they allow for precise tool alignment.

Calculate volumes of polyhedrons and cylinders for material weight estimation.

The Sine Bar Connection: Use the Sine function to determine the height of a gage block stack needed to set a specific angle.

Calculate the offset for a lathe tailstock to create a specific taper.

The "Dovetail Challenge" or Sine Bar Lab: A practical test where students use a physical sine bar, gage blocks, and a surface plate to verify the angle of a tapered workpiece using trigonometry.