Trigonometry: Solving Triangles
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The document summarizes two laws for solving triangles - the Law of Cosines and the Law of Sines. It also discusses an ambiguous case of the Law of Sines. The Law of Cosines can be used to find a missing side given two sides and the included angle, or to find a missing angle given all three sides. The Law of Sines can be used to find a missing side or angle given two angles and the side opposite one of them. The ambiguous case allows finding a missing angle given two sides and the angle opposite one of them.
Trigonometry: Solving Triangles
- 1. Law of the Cosines Law of the Sines - Ambiguous Case Area TRIGONOMETRY: SOLVING TRIANGLES
- 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. 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. 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. 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. Area Formula: t C c A a b B Have: two sides, included angle K = a b sin C two sides included angle