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§ 5-7

§ 5-7. Law of Sines. Goals. Solve triangle by using law of sines . Determine if a triangle has 0, 1, or 2 solutions. LAW OF SINES. When the measures of two sides of a triangle and the measure of angle opposite one of them are given, there may not always be one solution!.

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§ 5-7

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  1. § 5-7 Law of Sines

  2. Goals • Solve triangle by using law of sines. • Determine if a triangle has 0, 1, or 2 solutions

  3. LAW OF SINES

  4. When the measures of two sides of a triangle and the measure of angle opposite one of them are given, there may not always be one solution!

  5. One of the following will be true: • 1. No triangle exists • 2.Exactly one triangle exists • 3.Two triangles exist.

  6. Case #1 • When mA < 90º • If a = b sin A  one solution exists • If a > b sin A and a ≥ b  one solution exists • If a < b sin A  no solutions exist • If b sin A < a < b  two solution exists

  7. Case #2 • When mA≥ 90º • If a ≤ b  no solutions exist • If a > b  one solution exists

  8. Example #1 • Solve ∆ ABC if A = 32º14´, B= 57º40´, and c = 14.3 m. • C= • a= • b=

  9. Example #2 • Solve ∆ ABC if A = 58º, b=14 cm, and a =10 cm.

  10. Example #3 • Solve ∆ ABC if A= 72º14´ , b= 22 in, and a = 21 in. Round to the nearest minute and tenth.

  11. Example #4 • Solve ∆ ABC if A = 105º, b=55, and a =73

  12. Assignment • Page 324-326 • #’s 11-32 even, 46 • Due Monday

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