Chapter 6 trigonometric functions right triangle approach
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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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Chapter 6 trigonometric functions right triangle approach

Chapter 6 – Trigonometric Functions: Right Triangle Approach

Section 6.5 Law of Sines

6.5 - Law of Sines


Law of sines
Law of ApproachSines

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

6.5 - Law of Sines


Law of sines1
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
Definition Approach

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

6.5 - Law of Sines


Solving using saa
Solving Using SAA Approach

Solve the triangles below:

a) b)

6.5 - Law of Sines


Solving using asa
Solving Using ASA Approach

Solve the triangles below:

a) b)

6.5 - Law of Sines


The ambiguous case ssa
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
SSA – No Triangle Approach

6.5 - Law of Sines


Ssa one triangle
SSA – One Triangle Approach

6.5 - Law of Sines


Ssa two triangles
SSA – Two Triangles Approach

6.5 - Law of Sines


Examples ssa
Examples - SSA Approach

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

6.5 - Law of Sines


Examples ssa1
Examples - SSA Approach

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

6.5 - Law of Sines


Example pg 474
Example – pg. 474 Approach

6.5 - Law of Sines


Example pg 4741
Example – pg. 474 Approach

6.5 - Law of Sines


Example pg 4742
Example – pg. 474 Approach

6.5 - Law of Sines


Example pg 475
Example – pg. 475 Approach

6.5 - Law of Sines


More practice
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


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