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Math · Geometry · Unit 4

Unit 4: Right Triangle Trigonometry

Students build an understanding of ratios in right triangles, naming cosine, sine, and tangent as trigonometric ratios. They use trigonometry to find missing side lengths and angle measures and apply trigonometry to solve problems in context.

Worksheets

Every sheet has an answer key. Free to print, no login.

Unit
📝 Worksheet ✅ Answer guide
Concept
📝 Worksheet ✅ Answer key
Practice
Set 1
📝 Worksheet ✅ Answer key
Set 2
📝 Worksheet ✅ Answer key
Advanced
Set 1
📝 Worksheet ✅ Answer key
Set 2
📝 Worksheet ✅ Answer key

What this unit covers

A Angles and Steepness · 5 lessons
Goals
  • Comprehend that one acute angle of a right triangle determines all the ratios of the side lengths in that triangle.
  • Justify an estimated side length or angle measure using a table of ratios of side lengths of right triangles.
Lessons
  1. Angles and Steepness
  2. Half a Square (Optional)
  3. Half an Equilateral Triangle (Optional)
  4. Ratios in Right Triangles
  5. Working with Ratios in Right Triangles
B Defining Trigonometric Ratios · 5 lessons
Goals
  • Calculate angle measures in right triangles using arccosine, arcsine, and arctangent.
  • Calculate side lengths in right triangles using cosine, sine, and tangent.
  • Use trigonometry to solve problems in context.
Lessons
  1. Working with Trigonometric Ratios
  2. Applying Ratios in Right Triangles
  3. Sine and Cosine in the Same Right Triangle
  4. Trigonometry Squared
  5. Using Trigonometric Ratios to Find Angles
C Let’s Put It to Work · 2 lessons
Lessons
  1. Solving Problems with Trigonometry
  2. Approximating Pi
← Unit 3 See the whole map Unit 5 →

Adapted from the Illustrative Mathematics curriculum (v.360), licensed CC BY-NC 4.0. © Illustrative Mathematics.