Foundation
Vocabulary, marked diagrams, guided constructions, and reduced-complexity practice.
Open FoundationUnit 06 · Weeks 14, 15, 16, 17
Right Triangles, Trigonometry & Bearings
How do right-triangle relationships turn inaccessible lengths, heights, angles, and directions into measurable quantities?
Lesson sequence
8 visual, printable lessons
Lesson 01
Pythagorean Theorem & Its Converse
Prove or apply the relationship among the sides of a right triangle and use the converse for classification.
Lesson 02Special Right Triangles: 45-45-90
Use the side ratio 1:1:√2 and preserve exact radical form.
Lesson 03Special Right Triangles: 30-60-90
Use the side ratio 1:√3:2 and identify sides by their opposite angles.
Lesson 04Geometric Mean & Right-Triangle Altitudes
Use altitude-to-hypotenuse similarity and geometric mean relationships.
Lesson 05Sine, Cosine & Tangent Ratios
Use right-triangle relationships and trigonometric ratios to determine lengths, angles, heights, bearings, and directions.
Lesson 06Inverse Trigonometry & Angle Measure
Use inverse sine, cosine, or tangent to recover an angle from a side ratio.
Lesson 07Angles of Elevation and Depression
Use right-triangle relationships and trigonometric ratios to determine lengths, angles, heights, bearings, and directions.
Lesson 08Bearings, Vectors & Multi-Step Navigation
Translate compass bearings into right triangles or vectors and combine multiple legs of travel.
Core
Complete grade-level reasoning, calculation, proof, and printable evidence.
Open CoreExtended
Generalization, proof revision, optimization, design, and transfer.
Open Extended