7.6 Law of Sines

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7.6 Law of Sines
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Objective

• Use the Law of Sines to solve triangles and
  problems

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Law of Sines

• In trigonometry, we can use theLaw of Sines to
  find missing parts of triangles that are not
  right triangles.
• Law of Sines In ?ABC, sin A  sin B  sin
  C a b c

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Example 1a
Find p. Round to the nearest tenth.
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Example 1a
Law of Sines
Cross products
Use a calculator.
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Example 1b
Law of Sines
Cross products
Divide each side by 7.
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Example 1b
Solve for L.
Use a calculator.
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Your Turn
a. Find c. b. Find m?T to the nearest
degree in ?RST if r 12, t 7, and m?R 76.
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Solving a Triangle

• The Law of Sines can be used to solve a
  triangle, which means to find the measures of
  all of the angles and all of the sides of a
  triangle.

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Example 2a
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Example 2a
Angle Sum Theorem
Add.
Subtract 120 from each side.
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Example 2a
To find d
Law of Sines
Substitute.
Cross products
Divide each side by sin 8.
Use a calculator.
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Example 2a
To find e
Law of Sines
Substitute.
Cross products
Divide each side by sin 8.
Use a calculator.
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Example 2b
We know the measure of two sides and an angle
opposite one of the sides.
Law of Sines
Cross products
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Example 2b
Divide each side by 16.
Solve for L.
Use a calculator.
Angle Sum Theorem
Substitute.
Add.
Subtract 116 from each side.
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Example 2b
Law of Sines
Cross products
Use a calculator.
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Your Turn
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Example 3
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Example 3
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Example 3
Law of Sines
Cross products
Use a calculator.
Answer The length of the shadow is about 75.9
feet.
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Your Turn
A 5-foot fishing pole is anchored to the edge of
a dock. If the distance from the foot of the pole
to the point where the fishing line meets the
water is 45 feet, about how much fishing line
that is cast out is above the surface of the
water?
Answer About 42 feet of the fishing line that
is cast out is above the surface of the water.
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Assignment

• Pre-AP Geometry Pg. 381 15, 16 32 evens, 42
  
• Geometry Pg. 381 15, 16 28 evens