Law of Sines

Solving Triangles: In order to do so, you need 3 pieces of Information.

Given a Right Triangle.

Use trigonometry (Sine, cosine, tangent) to find a missing side or angle,

Use the pythagorean, theorem when you have

2 sides given.

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Non-Right Triangle when You are given 2 sides and the angle between them. (SAS)

1. Find the 3rd Side using

the 1st version of the

Law of Cosines.

2. Then find an angle using. law of Sines,
3. Use 180° and other 2 angles to find the lost angle.

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Non-Right Triangle Where you have all 3 sides Given (sss)

1. Find one angle using 2nd Version of the Law of Cosines.
2. Find another angle using law of Sins.
3. Use 180° to find last angle.

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Non-Right Triage where you are given a Side-angle opposite pair.

1. Use Law of Sines to find missing info.
2. Repeat as necessary.

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When given SAS

1. Start with 1st version of the Law of cosines to find the 3rd side
2. Then use Law of Sines to find an angle
3. Add angles and subtract from 180 to find 3rd angle

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When given SSS

1. Start with version 2 of the law of cosines to find a missing angle
2. Then use the law of sines to find another angle
3. End with 180 rule to find last angle

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When Given a Side-Angle pair (AAS, ASA, SSA)

1. Either use the Law of sines to find a missing angle or find the 3rd angle using 180 rule
2. Use law of sines to find any other missing sides or 180 rule to find an angle

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