CCSS.Math.Content.HSG-SRT.D.10
The standard
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
Common Core State Standards for Mathematics
What this standard means
Students need to explain why the sine and cosine rules work, not just plug numbers into them. They should use triangles, altitudes, right triangle trig, and algebra to build a proof. Then they need to choose the right rule for a given triangle problem, including missing sides, missing angles, and ambiguous cases.
Mastery looks like clear setup, correct rule choice, accurate solving, and a reasonableness check on the answer. Students often get stuck deciding which rule fits the given information. They also mix up opposite pairs, round too early, or miss the second possible triangle in the SSA case.
Ways to teach it
- Hands-on activity: Have students draw two different triangles with SSA measurements using straws and brads, then measure both possible angle outcomes.
- Discussion or writing prompt: Ask students to explain when they would use the sine rule instead of the cosine rule, using two sample triangles.
- Quick assessment: Give three triangles with labeled givens, and have students write only the correct equation to start each problem.
- Real-world connection: Use a map, two landmarks, and one measured angle to find an inaccessible distance across a pond or field.
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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.HSF-TF.C.9
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
- CCSS.Math.Content.HSF-TF.C
Prove and apply trigonometric identities
- CCSS.Math.Content.HSG-SRT.D.11
(+) 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, result...