Final answer:
Using the triangle inequality theorem, the missing side x of the triangle must be greater than 3.6 ft and less than 21.4 ft. Without additional information, the values 8.8 ft and 9.5 ft are both possible answers as they satisfy the theorem's conditions.
Step-by-step explanation:
To find the value of the missing side labeled 'x' in a triangle with given sides of 8.9 ft and 12.5 ft, we must identify whether we are dealing with a right triangle and can therefore apply the Pythagorean theorem or if we are simply using the triangle inequality theorem. Since we are not expressly told if it is a right triangle, the safest assumption here would be to use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, if we assume that 8.9 ft and 12.5 ft are the two longer sides of the triangle, the missing side 'x' must be less than their sum but greater than their difference:
- 8.9 ft + x > 12.5 ft or x > 12.5 ft - 8.9 ft
- 12.5 ft + 8.9 ft > x or x < 21.4 ft
Therefore, x must be greater than 3.6 ft and less than 21.4 ft. Upon reviewing our answer choices, we can immediately see that option b) 8.8 ft and option c) 9.5 ft are within this range.
However, to narrow it down further, we should consider the lengths in context. 1.3 ft (option a) seems unlikely as it's much smaller than the other sides, and 15.3 ft (option d) would make this side the longest, which goes against the context of the question assuming x is the side opposite the largest angle.