5.5

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5.5 Use Inequalities in a Triangle

• 1. Draw an obtuse scalene triangle.
• Measure all the sides and all of the angles.
• Find the largest angle and the largest side and
  mark them in one color.
• Find the smallest angle and the smallest side and
  mark them in a different color than in 3.

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5.5 Use Inequalities in a Triangle
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5.5 Use Inequalities in a Triangle
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5.5 Use Inequalities in a Triangle

• Example 1
• Three wooden beams will be nailed together to
  form a brace for a wall. The bottom edge of the
  brace is about 8 feet, and the sides are about 12
  feet and 14 feet. One of the angles measures 86
  degrees and the other measures about 35 degrees.
  What is the angle measure opposite the largest
  side of the brace?

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5.5 Use Inequalities in a Triangle

• Example 2
• You are constructing a stage prop that shows a
  large triangular mountain. The bottom edge of
  the mountain is about 27 feet long, the left
  slope is about 24 feet long, and the right slope
  is about 20 feet long. You are told that one of
  the angles is about 46 degrees and one is about
  59 degrees. What is the angle measure of the
  peak of the mountain?

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5.5 Use Inequalities in a Triangle

• The Triangle Inequality
• Not every group of three segments can be used to
  form a triangle. The lengths of the segments
  must fit a certain relationship.

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5.5 Use Inequalities in a Triangle
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5.5 Use Inequalities in a Triangle

• Example 3
• A triangle has one side of length 12 and another
  of length 8. Describe the possible lengths of
  the third side.

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5.5 Use Inequalities in a Triangle

• Example 4
• Is it possible to construct a triangle with the
  given side lengths?
• 6, 7, 11 3, 6, 9 28, 34,
  39

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5.5 Use Inequalities in a Triangle

• Example 5
• Describe the possible values of x.