Solving NonRight Triangles

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Section 8.2

• Solving Non-Right Triangles

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If none of the angles of a triangle is a right
angle, the triangle is called oblique.
Obtuse
Acute
To solve an oblique triangle means to find the
lengths of its sides and the measurements of its
angles.
3
A
S
A
ASA
S
A
A
SAA
CASE 1 ASA or SAA
4
S
A
S
CASE 2 SSA (Does not guarantee
uniqueness) Special case we will explore at end
of lecture
5
S
A
S
CASE 3 SAS
6
S
S
S
CASE 4 SSS
7
Name the case
5
47o
7

• SSS
• SAS
• SSA
• ASA
• AAA
• AAS

8
Theorem Law of Sines
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Proof (one case for law of sines)
a
b
h
10
c
b
5
11
3
5
a
No triangle with the given measurements! Side of
length 3 not long enough to be opposite of 50
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Which numbers are not allowed in Law Of Sines
problem for sin a?(1) -0.7 (2) 0 (3) 0.7 (4)
1.4(5) 0.35(6) -0.35(7) All are OK
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Multiple Solutions CASE
S
S
A
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Multiple (2) Solutions Problem (SSA)

• Given a30 a8 b10

10
10
8
OR
8
30
30
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Multiple (2) Solutions Problem (ASS)

• Given a30 a8 b10

8.68
10
10
8
OR
8
30
38.68
30
141.32
So, 3rd angle is 180 30 38.68 111.32
Finding 3rd side