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Section 6.5 Law of Sines

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# Section 6.5 Law of Sines - PowerPoint PPT Presentation

Chapter 6 – Trigonometric Functions: Right Triangle Approach. Section 6.5 Law of Sines. Law of Sines. Used for oblique triangles (triangles that do not contain right angles). Law of Sines. We have two possible cases for the law of sines . Case 1 – One side and two angles (ASA or SAA)

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Chapter 6 – Trigonometric Functions: Right Triangle Approach

### Section 6.5 Law of Sines

6.5 - Law of Sines

Law of Sines
• Used for oblique triangles (triangles that do not contain right angles).

6.5 - Law of Sines

Law of Sines
• We have two possible cases for the law of sines.
• Case 1 – One side and two angles (ASA or SAA)
• Case 2 – Two sides and the opposite angle to one of those sides (SSA)

6.5 - Law of Sines

Definition
• Law of Sines works when we have SAA or ASA.

6.5 - Law of Sines

Solving Using SAA

Solve the triangles below:

a) b)

6.5 - Law of Sines

Solving Using ASA

Solve the triangles below:

a) b)

6.5 - Law of Sines

The Ambiguous Case (SSA)

SSA is called an ambiguous case because the given information can result in zero, one, or two triangles.

6.5 - Law of Sines

SSA – No Triangle

6.5 - Law of Sines

SSA – One Triangle

6.5 - Law of Sines

SSA – Two Triangles

6.5 - Law of Sines

Examples - SSA
• Solve ABC if A = 50, a = 10, and b = 20.

6.5 - Law of Sines

Examples - SSA
• Solve ABC if A = 40, a = 54, and b = 62.

6.5 - Law of Sines

Example – pg. 474

6.5 - Law of Sines

Example – pg. 474

6.5 - Law of Sines

Example – pg. 474

6.5 - Law of Sines

Example – pg. 475

6.5 - Law of Sines

More Practice
• Sketch the triangle. Use the Law of Sines to solve for all possible triangles that satisfy the given conditions.

6.5 - Law of Sines