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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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### Section 6.5 Law of Sines

6.5 - Law of Sines

Law of ApproachSines

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

6.5 - Law of Sines

Law of ApproachSines

• 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 Approach

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

6.5 - Law of Sines

Solving Using SAA Approach

Solve the triangles below:

a) b)

6.5 - Law of Sines

Solving Using ASA Approach

Solve the triangles below:

a) b)

6.5 - Law of Sines

The Ambiguous Case (SSA) Approach

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 Approach

6.5 - Law of Sines

SSA – One Triangle Approach

6.5 - Law of Sines

SSA – Two Triangles Approach

6.5 - Law of Sines

Examples - SSA Approach

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

6.5 - Law of Sines

Examples - SSA Approach

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

6.5 - Law of Sines

Example – pg. 474 Approach

6.5 - Law of Sines

Example – pg. 474 Approach

6.5 - Law of Sines

Example – pg. 474 Approach

6.5 - Law of Sines

Example – pg. 475 Approach

6.5 - Law of Sines

More Practice Approach

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

6.5 - Law of Sines