Triangles and trigonometry: a learning progression
Use triangle properties, similarity, and right-triangle ratios to calculate unknown lengths and angles.
Before you begin
Understand angle totals, ratios, squares, and square roots.
Readiness depends on the ideas you can use, not only your age or grade. Start earlier in the sequence when an example feels unfamiliar.
How the skill develops
- Use triangle angle sums and congruence or similarity conditions.
- Identify the hypotenuse before applying the Pythagorean theorem.
- Choose sine, cosine, or tangent from the sides relative to an angle.
- Extend to unit-circle values, identities, and non-right-triangle relationships.
What grade is this taught?
Our catalog includes this progression from grade 5 through grade 12. That is a map of the practice available here, not a rule that every school uses the same schedule. Earlier grades may introduce models that later grades formalize.
The sequence is our teaching organization, informed by the published curriculum reference. High-school courses and calculus enrollment vary; check your school’s syllabus for placement decisions.
Build your next practice steps
Mark skills you already feel comfortable with. We’ll suggest the next unchecked skills in this sequence. This is a self-selected path, not a test score.