To find the largest two-digit number using the digits from the set {3, 4, 9, 8, 2}, we want to select the two highest digits available.
The highest digits in the set are 9 and 8.
- By arranging these digits, the two-digit numbers we can form are 98 and 89.
- The largest of these is 98.
Therefore, the largest two-digit number that can be made from using two of the digits 3, 4, 9, 8, and 2 is 98.