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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

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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


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