Chapter 9 section 2

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Chapter 9 section 2

• Law of Sines

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If none of the angles of a triangle is a right
angle, the triangle is called oblique.
All angles are acute
Two acute angles, one obtuse angle
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To solve an oblique triangle means to find the
lengths of its sides and the measurements of its
angles.
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FOUR CASES
CASE 1 One side and two angles are known (SAA or
ASA).
CASE 2 Two sides and the angle opposite one of
them are known (SSA).
CASE 3 Two sides and the included angle are
known (SAS).
CASE 4 Three sides are known (SSS).
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A
S
A
ASA
S
A
A
SAA
CASE 1 ASA or SAA
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S
A
S
CASE 2 SSA
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S
A
S
CASE 3 SAS
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S
S
S
CASE 4 SSS
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The Law of Sines is used to solve triangles in
which Case 1 or 2 holds. That is, the Law of
Sines is used to solve SAA, ASA or SSA triangles.
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Theorem Law of Sines
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c
b
5
13
b
12
a
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3
a
5
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Two triangles!!
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Triangle 1
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Triangle 2
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3
5
a
No triangle with the given measurements!