Use a Matched Length Ratio
Corresponding side lengths of similar triangles share one scale factor.
About 20 minutes, plus any extended practice
Open lesson 1Geometry: Similarity and Right-Triangle Ratios
Similarity preserves angle measures and corresponding length ratios. Right triangles with the same acute angle are similar, explaining why sine, cosine and tangent depend on an angle rather than the triangle’s overall size.
Before you begin
- Use ratios and proportions; identify opposite leg, adjacent leg and hypotenuse.
Choose by skill rather than age alone. Read with an adult when useful, revisit a lesson, or explore another grade.
Follow the lesson sequence
Use Opposite over Hypotenuse
For an acute angle in a right triangle, sine is opposite-leg length divided by hypotenuse length.
About 20 minutes, plus any extended practice
Open lesson 2Use Adjacent Leg over Hypotenuse
Cosine compares the leg touching an acute reference angle with the hypotenuse.
About 20 minutes, plus any extended practice
Open lesson 3Use Opposite over Adjacent Leg
Tangent is the ratio of the opposite leg to the adjacent leg for an acute angle.
About 20 minutes, plus any extended practice
Open lesson 4Review and transfer
After the lessons, try 4 new review cases and a practical task. Each answer has an explanation and a link back to the related lesson.
Open the unit reviewGuest answers are temporary. Keep your own paper or document; this unit does not certify completion or record a school grade.
Topic references
- California CCSS mathematics topic reference: topic reference — Geometry: Similarity and Right-Triangle Ratios
These references informed the topic selection. They do not certify complete standards alignment.