Essential question: How do I solve oblique triangles?

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Presentation transcript:

Essential question: How do I solve oblique triangles? How do I deal with “SSA” when solving oblique triangles? “the ambiguous case”

First, determine what case you have. (ASA, AAS, SSA, etc.) Law of Sines (“plug & chug”) determine # of solutions use the Law of Sines to find them.

SSA Ex. 3 Solve ABC. A = 42°, a = 22 inches, & b = 12 inches a b 21.41° b = 12 in A c = 29.40 in C = 116.59º C = 180º - 42º - 21.41º = 116.59º c = 29.40

Solving for 2 triangles: Determine what you are given (SSS, SAS, SSA, etc) Find all info as usual Go back to the 1st angle you found… subtract it from 180 (180 - angle) Add this new angle to the given angle Compare that answer to 180 * if it is < 180 you have another triangle * if it is > 180 you have only 1 triangle

SSA Ex. 5 A = 20.5°, a = 12, and b = 31 A = 20.5° a = 12 b a B1 = 64.78° b = 31 A C1 = 94.72º c1 = 34.15 C = 180º - 20.5º - 64.78º = 94.72º c = 34.15

SSA Ex. 5 A = 20.5°, a = 12, and b = 31 Solution #2 b A = 20.5° a = 12 115.22° b = 31 A C2 = 44.28º c2= 23.93 Remember B2 = 180 - B1 Since 115.2 + A is less than 180 there are 2 triangles! B2 = 180 - 64.78 = 115.22 C = 180º - 20.5º - 115.22º = 44.28º c = 23.93

Ex. 4 a = 15, b = 25, and A = 85° SSA No solution! Yea! Error!!!