Chapter 6 – Trigonometric Functions: Right Triangle Approach

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Presentation transcript:

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.

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