Trigonometry: Section 5.6 The Law of Sines

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Trigonometry Section 5.6The Law of Sines

• Objectives of this Section
• Solve SAA or ASA Triangles
• Solve SSA Triangles
• Solve Applied Problems

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If none of the angles of a triangle is a right
angle, the triangle is called oblique.
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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The Law of Sines is used to solve triangles in
which Case 1 or 2 holds. The Law of Sines is
used to solve SAA, ASA or SSA triangles.
Law of Sines
5
c
b
5
6
b
12
a
7
3
a
5
8
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Two triangles!!
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Triangle 1
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Triangle 2
12
3
5
a
No triangle with the given measurements!
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Area of Triangles (2 cases)

• If 2 sides are known (SAS)
• K ½ bc Sin A (included angle)
• K ½ ac Sin B (included angle)
• K ½ ab Sin C (included angle)

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Area of Triangles (2 cases cont.)

• If 2 angles are known
• K ½ a2 Sin B Sin C
• Sin A
• K ½ b2 Sin A Sin C
• Sin B
• K ½ c2 Sin A Sin B
• Sin C

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Ex. 2 Find the area if c 16.5, b 21.2, ?A
25
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Ex. 3 Find the area if j 45.7, ?K 111.1,
?L 27.3
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Assignment

• Section 5-4
• 1-8 from projector

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Assignment

• Page 316
• 12-24 even
• 32