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Understanding the Law of Cosines: Solving SAS and SSS Triangles in Trigonometry

In this section of Sullivan's Algebra and Trigonometry, we explore the Law of Cosines, a powerful tool for solving oblique triangles. We focus on two key cases: Case 1 for SAS triangles, where two sides and the included angle are known, and Case 2 for SSS triangles, with all three sides provided. We'll also apply these principles to solve various applied problems, enhancing our understanding of triangle solutions in real-world scenarios. Master these techniques to effectively tackle triangle-related questions with confidence.

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Understanding the Law of Cosines: Solving SAS and SSS Triangles in Trigonometry

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  1. Sullivan Algebra and Trigonometry: Section 8.3The Law of Cosines • Objectives of this Section • Solve SAS Triangles • Solve SSS Triangles • Solve Applied Problems

  2. We use the Law of Sines to solve CASE 1 (SAA or ASA) and CASE 2 (SSA) of an oblique triangle. The Law of Cosines is used to solve CASES 3 and 4. CASE 3:Two sides and the included angle are known (SAS). CASE 4: Three sides are known (SSS).

  3. Law of Cosines

  4. 3 a 4

  5. 3 2.57 4

  6. 5 3 7

  7. 5 3 7

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