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Trigonometry: Solving Triangles

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Formulas with triangles/descriptions for Law of the Cosines, Law of the Sines, and the Area Formula

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  • simple, to the point. thanks! :)
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  • This is an excellent tool to use as a part of intro to trig.!!!
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Trigonometry: Solving Triangles

  1. 1. <ul><li>Law of the Cosines </li></ul><ul><li>Law of the Sines </li></ul><ul><li>- Ambiguous Case </li></ul><ul><li>Area </li></ul>TRIGONOMETRY: SOLVING TRIANGLES
  2. 2. Law of Cosines: Have: two sides, included angle Solve for: missing side ( missing side ) 2 = ( one side ) 2 + ( other side ) 2 – 2 ( one side )( other side ) cos( included angle ) c 2 = a 2 + b 2 – 2 a b cos C C c A a b B
  3. 3. Law of Cosines: C c A a b B a 2 + b 2 – c 2 2ab cos C = Have: three sides Solve for: missing angle Missing Angle Side Opposite Missing Angle
  4. 4. Law of Sines: C c A a b B Have: two angles, one side opposite one of the given angles Solve for: missing side opposite the other given angle Missing Side a sin A = b sin B
  5. 5. Ambiguous Case: ( Special Case of Law of Sines ) C c A a b B Have: two sides, angle opposite one of the given sides Solve for: missing angle opposite the other given side Missing Angle a sin A = b sin B
  6. 6. Area Formula: t C c A a b B Have: two sides, included angle K = a b sin C two sides included angle

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