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.