The problem requires finding the range of possible values for $x$, the unknown side of a triangle, using the triangle inequality theorem.

Steps to Solve:

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. For the triangle in the question, with two sides of 2.8 and one side $x$:

1. $2.8 + 2.8 > x$ $x < 5.6$

2. $2.8 + x > 2.8$ $x > 0$

3. $x + 2.8 > 2.8$ $x > 0$

Combining the Results:

Since $x$ must satisfy all these conditions, the range is: $2.8 < x < 5.6$

Final Answer:

The range of possible sizes for $x$ is: $\boxed{2.8 < x < 5.6}$

Would you like a detailed breakdown of any specific step or additional examples?

Related Questions:

1. How does the triangle inequality theorem apply to real-world problems?
2. What happens if $x = 2.8$ or $x = 5.6$? Why are they excluded?
3. Can the triangle inequality theorem help determine if a triangle is scalene, isosceles, or equilateral?
4. How would the range change if one of the sides were longer, say 3.5 instead of 2.8?
5. Could a right triangle have $x$ in this range, given $a = 2.8$ and $b = 2.8$?

Tip:

Always ensure the triangle inequality theorem is satisfied before assuming a set of side lengths can form a triangle.