Short Answer 
The problem involves three segments of lengths 8 units, 10 units, and 6 units. Using the Pythagorean theorem, we find that the length of the segment is 6 units after confirming that c² = a² + b² leads to the calculation c = √(10² + 8²).
Step 1: Identify the Segments
Start by recognizing the segments involved in your problem. You have three segments with the following lengths:
- Segment ef = 8 units
- Segment ed = 10 units
- Segment fa = 6 units
Step 2: Apply Pythagorean Theorem
Utilize the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c²) is equal to the sum of the squares of the other two sides (a² and b²). For this problem:
- c = Length of segment (to find)
- a = 10 units
- b = 8 units
Step 3: Solve for Length of the Segment
Complete the calculations based on your previous formula. Substitute the values:
- c² = √(10² + 8²)
- c² = √(100 + 64)
- c² = √(36)
- c = 6 units