Lesson 3: The Heart of the Shop—Right Triangle Trig
Duration of Days: 4
Lesson Objective
SWBAT: Identify the Opposite, Adjacent, and Hypotenuse sides relative to a given angle ?.
Use Sine, Cosine, and Tangent ratios to solve for missing angles and side lengths on a part drawing.
How can one known angle and one known side give us every other dimension on a part?
Why is the Tangent function the most used ratio in the machine shop?
Trigonometry, ? (Theta), Sine, Cosine, Tangent, SOH-CAH-TOA, inverse function, ratio, adjacent, opposite.
CTE.MFG.B.09 (Use trigonometric functions to solve manufacturing problems)
CCSS.Math.HSG.SRT.C.8 (Trig ratios).
This is the most critical math lesson in the course. Students learn SOH-CAH-TOA to find unknown angles and side lengths. The purpose is to provide the math needed for nearly all complex machining setups.
DOK Level: 3 (Strategic Thinking)
Support: Provide a "Trig Triangle" visual aid that helps students decide which function to use based on what information they have.
Extension: Introduce Oblique Triangles (Law of Sines/Cosines) for triangles that do not have a 90-degree angle.
"The Trig Blueprint" – A drawing with multiple missing angles and lengths that can only be found using SOH-CAH-TOA.