5.5 – Use Inequalities in a Triangle
1. Draw an obtuse scalene triangle.
2. Measure all the sides and all of the angles.
3. Find the largest angle and the largest side
and mark them in one color.
4. Find the smallest angle and the smallest
side and mark them in a different color than
in #3.
5.5 – Use Inequalities in a Triangle
5.5 – Use Inequalities in a Triangle
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?
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?
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.
5.5 – Use Inequalities in a Triangle
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.
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
5.5 – Use Inequalities in a Triangle
Example 5:
Describe the possible values of x.