Answer:
30.5 feet ≤ AC ≤ 56.1 feet
Explanation:
To find the range of the distance between point A and point C in triangle ABC, we can use the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the third side.
In this case, we have:
The distance between A and B is 43.3 feet.
The distance between B and C is 12.8 feet.
Now, we want to find the range for the distance between A and C, which is represented by side AC. The triangle inequality for side AC is:
AC ≤ AB + BC
Substitute the given values:
AC ≤ 43.3 feet + 12.8 feet
AC ≤ 56.1 feet
So, the maximum possible distance between A and C (AC) is 56.1 feet.
Now, to find the minimum possible distance between A and C, we need to consider the possibility where the three points are collinear, and AC is the difference between AB and BC:
AC ≥ |AB - BC|
AC ≥ |43.3 feet - 12.8 feet|
AC ≥ |30.5 feet|
AC ≥ 30.5 feet
So, the minimum possible distance between A and C (AC) is 30.5 feet.
Therefore, the range for the distance between A and C is greater than or equal to 30.5 feet and less than or equal to 56.1 feet.
Mathematically;
30.5 feet ≤ AC ≤ 56.1 feet