Mat 161 PreCalculus

1
Mat 161 - PreCalculus

• Law of Sines
• (Section 7.1)

2
Law of Sines

• To solve an arbitrary triangle ABC, we can
• Use the following law

C
a
b
A
B
c
3
Law of Sines

• Example Let A 42, C 96and c 12m.
• Solve the triangle. Give each missing
• quantity to the nearest tenth.

4
Law of Sines

• Example
• Let A 12, a 7 ft and b 28ft.
• Solve the triangle. How many such
• triangles can there be? Give each missing
• quantity to the nearest tenth.

5
Law of Sines

• Area of a Triangle
• A ½ ab sin C ½ ac sin B ½ bc sin A
• Example Find the area of the triangle

43o
2.6
6.8
6

• Law of Cosines
• (Section 7.2)

C
Given an arbitrary triangle ABC, we have that 1)
2) 3)
a
b
B
A
c
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Law of Cosines

• Example
• Let A 42, b 9 m and c 12m.
• Solve the triangle. Give each missing
• quantity to the nearest tenth.

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Law of Cosines

• Example Let B 42, b 5 and c 12.
• Solve the triangle. Give each missing
• quantity to the nearest tenth.

9
Law of Cosines

• Example Let a 7, b 8 and c 10.
• Solve the triangle. Give each missing
• quantity to the nearest tenth.

10
Law ofSine

• Reference
• Algebra and Functions
• Blitzer
• 3rd Edition