6.5 - Law of Sines

Section 6.5 Law of Sines

Chapter 6 – Trigonometric Functions: Right Triangle Approach

6.5 - Law of Sines

Law of SinesUsed for oblique triangles (triangles that do not

contain right angles).

6.5 - Law of Sines

Law of SinesWe 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

DefinitionLaw of Sines works when we have SAA or ASA.

6.5 - Law of Sines

Solving Using SAASolve the triangles below:a) b)

6.5 - Law of Sines

Solving Using ASASolve 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 - SSASolve ABC if A = 50, a = 10, and b = 20.

6.5 - Law of Sines

Examples - SSASolve 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 PracticeSketch the triangle. Use the Law of Sines to solve

for all possible triangles that satisfy the given conditions. 22 , 95 , 420

a 28, 15, 110

a 30, 40, 37

a 20, 45, 125

b 45, 42, 38

A B a

b A

c A

c A

c C

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