CCSS.Math.Content.HSG-SRT.D.11
The standard
(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
Common Core State Standards for Mathematics
What this standard means
Students need to choose and use the Law of Sines or Law of Cosines to find missing side lengths and angle measures in any triangle, not just right triangles. They should connect the given information, such as SAS, SSS, ASA, AAS, or SSA, to the right formula and solve carefully.
Mastery means students can draw and label a triangle from a situation, pick a method, solve, and check if the answer makes sense. Common trouble spots are using the wrong law, mixing up opposite sides and angles, rounding too early, and missing the possible second triangle in SSA cases.
Ways to teach it
- Hands-on activity: Give pairs straws, angle rulers, and string to build an SSA triangle and test when one, two, or no triangles work.
- Discussion prompt: Ask students, “What information tells you to use Law of Sines instead of Law of Cosines?” and require a labeled sketch.
- Quick assessment: Give three labeled triangles, one ASA, one SAS, one SSS, and ask students to choose the law and solve one missing part.
- Real-world connection: Have students model two observers measuring angles to a flagpole, then use Law of Sines to find its distance from one observer.
Plan a lesson for CCSS.Math.Content.HSG-SRT.D.11
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Related standards
- CCSS.Math.Content.HSF-TF.B.7
(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms...
- CCSS.Math.Content.HSG-SRT.D.10
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
- CCSS.Math.Content.HSF-TF.C.9
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
- CCSS.Math.Content.HSG-SRT.C.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.