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4-7a Law of Sines and the Law of Cosines

Rigor: You will learn how to use the Law of Sines and Cosines to solve right triangle problems. Relevance: You will be able to use the Law of Sines and Cosines to solve real world problems. . 4-7a Law of Sines and the Law of Cosines. Cases:. ASA or SAA 2 SSA 3 SAS 4 SSS.

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4-7a Law of Sines and the Law of Cosines

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  1. Rigor:You will learn how to use the Law of Sines and Cosines to solve right triangle problems.Relevance:You will be able to use the Law of Sines and Cosines to solve real world problems.

  2. 4-7a Law of Sines and the Law of Cosines

  3. Cases: • ASA or SAA 2 SSA 3 SAS 4 SSS LAW OF SINES LAW OF COSINES

  4. Triangles: • AAS – 2 angles, non-included side Creates 1 triangle • ASA – 2 angles, included side Creates 1 triangle

  5. Law of Sines:

  6. Example 1: Solve ∆ABC. Round side lengths to the nearest tenth and angle measures to the nearest degree. C = 180° – 35° – 103° = 42° Use law of Sines to find a and c. , , and C = 42°

  7. Two Triangle One Triangle No Triangle One Triangle No Triangle One Triangle

  8. Example 3a: Find all solutions for the triangle. If no solution exists, write no solution. Round side lengths to the nearest tenth and angle measures to the nearest degree. a. a = 15, c = 12, A = 94° A is obtuse and a > c one solution exists. Use law of Sines to find C and b. , C , and B 33°

  9. Example 3b: Find all solutions for the triangle. If no solution exists, write no solution. Round side lengths to the nearest tenth and angle measures to the nearest degree. a. a = 9, b = 11, A = 61° A is acute and a < b so find h. No triangle can be formed so there is no solution.

  10. math! • 4-7a Assignment: TX p298, 2-24 even

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