To solve this, we can use the Pythagorean theorem, which states that for a right triangle:

$a^2 + b^2 = c^2$

where $a$ and $b$ are the legs (the shorter sides) of the triangle, and $c$ is the hypotenuse (the longest side).

Now, let's go through each option:

1. 5, 9, 12.3
   Check if $5^2 + 9^2 = 12.3^2$:
   $5^2 + 9^2 = 25 + 81 = 106$ $12.3^2 = 151.29$ Since 106 does not equal 151.29, this set does not form a right triangle.

2. 9, 40, 41
   Check if $9^2 + 40^2 = 41^2$:
   $9^2 + 40^2 = 81 + 1600 = 1681$ $41^2 = 1681$ This is correct! So, this is a valid set.

3. 12.5, 7.5, 10
   Check if $12.5^2 + 7.5^2 = 10^2$:
   $12.5^2 + 7.5^2 = 156.25 + 56.25 = 212.5$ $10^2 = 100$ This is incorrect. So, this is not a valid set.

4. 14, 15, 16
   Check if $14^2 + 15^2 = 16^2$:
   $14^2 + 15^2 = 196 + 225 = 421$ $16^2 = 256$ This is incorrect. So, this is not a valid set.

5. 46.1, 55, 30
   Check if $46.1^2 + 55^2 = 30^2$:
   $46.1^2 + 55^2 = 2127.21 + 3025 = 5152.21$ $30^2 = 900$ This is incorrect. So, this is not a valid set.

6. 98, 15, 84
   Check if $98^2 + 15^2 = 84^2$:
   $98^2 + 15^2 = 9604 + 225 = 9829$ $84^2 = 7056$ This is incorrect. So, this is not a valid set.

The correct option is:

• 9, 40, 41

Would you like further explanation or help with a related topic? Here are some related questions to explore:

1. What is the relationship between the Pythagorean theorem and trigonometry?
2. Can you find the perimeter and area of a right triangle using the Pythagorean theorem?
3. How can you use the Pythagorean theorem for 3D shapes?
4. What are Pythagorean triples and how do they relate to this problem?
5. Can the Pythagorean theorem be applied to non-right triangles in some way?

Tip: When testing potential side lengths, always check that the square of the longest side equals the sum of the squares of the other two sides.