Geometry Lesson

Discovering SOH-CAH-TOA: NASA Satellite Dish Shadow Ratios

Shared by A STEM Educator

9th-10th GradeThin-SlicingHSG.SRT.C.6, HSG.SRT.C.850 min

Learning Objective

Students will discover that the ratio of specific pairs of sides in a right triangle depends only on the angle (not the triangle's size), name these ratios sine, cosine, and tangent, and apply SOH-CAH-TOA to find missing sides in right triangles (HSG.SRT.C.6, HSG.SRT.C.8).

Lesson Overview

Students discover that the ratios of sides in similar right triangles are constant for a given angle, then name and apply sine, cosine, and tangent to solve real-world problems set in the context of a NASA satellite dish casting shadows.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors)
Rulers and protractors
Scientific calculators
Random grouping cards
Printed graphic organizer (scaffoldedSupport)

Scaffolded Task Progression

1Task 1

Below are two right triangles. Both have the same 40° angle at their base. Measure each side with your ruler (in cm), then fill in the table.

[ Interactive graph / diagram — available in the full lesson ]

A NASA dish and a scale model are both tilted at 40°. Does the ratio opposite÷hypotenuse change between the two sizes?

2Task 2

Now try a 60° angle. Both triangles below share the same 60° base angle but have different sizes. Compute the three ratios for each triangle and record them.

[ Interactive graph / diagram — available in the full lesson ]

Are the ratios the same as the 40° triangles from Task 1? What does this tell you?

Unlock the full lesson

See all 7 scaffolded tasks, the full answer key, warm-up, exit slip, and a print-ready version — free to start.

Create a free account

Already have an account? Sign in

Make it your own

Like this lesson but want to tweak it?

Make an editable copy and adjust the tasks, warm-up, and answer key to fit your class — no need to start from scratch.

Generate a new lesson