CCSS.Math.Content.HSG-SRT.D
The standard
Apply trigonometry to general triangles
Common Core State Standards for Mathematics · High School — Geometry
What this standard means
Students need to use trigonometry beyond right triangles. They should choose and apply the Law of Sines, Law of Cosines, and the triangle area formula using two sides and the included angle. They also need to decide when a triangle has one solution, two solutions, or no solution.
Mastery looks like reading a triangle problem, sketching it, labeling knowns, choosing the right formula, and explaining whether the answer is reasonable. Students often get stuck on the ambiguous case, mixing up included and non-included angles, and using degrees or radians incorrectly on a calculator.
Ways to teach it
- Hands-on activity: Give pairs straws, string, and protractors to build SSA triangles and test when zero, one, or two triangles form.
- Prompt: Ask students to explain which formula they would use for AAS, SAS, SSA, and SSS triangles, and why.
- Quick assessment: Show three labeled triangles and have students write only the correct formula setup, not the final answer.
- Real-world connection: Have students solve a surveying problem finding the width of a pond using two measured distances and one angle.
Plan a lesson for CCSS.Math.Content.HSG-SRT.D
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Related standards
- CCSS.Math.Content.HSG-SRT.C
Define trigonometric ratios and solve problems involving right triangles
- CCSS.Math.Content.HSG-SRT.B.4
Prove theorems about triangles.
- CCSS.Math.Content.HSF-TF.C
Prove and apply trigonometric identities
- CCSS.Math.Content.HSG-SRT.C.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.