This is a right triangle problem where we need to find the length of the hypotenuse $c$, given the lengths of the other two sides $a = 20 \, \text{m}$ and $b = 15 \, \text{m}$.

We can solve this using the Pythagorean theorem, which states that:

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

Let's calculate the value of $c$:

$c^2 = 20^2 + 15^2 = 400 + 225 = 625$

$c = \sqrt{625} = 25 \, \text{m}$

So, the correct value for $c$ is 25 meters.

Would you like further details or have any other questions?

Here are 5 related questions to expand on this concept:

1. How does the Pythagorean theorem apply to non-right triangles?
2. What happens if one of the sides is missing and the hypotenuse is known?
3. Can you use the Pythagorean theorem in three dimensions?
4. How can the sine, cosine, and tangent functions help in solving triangle problems?
5. What are the applications of right triangles in real life?

Tip: When solving right triangle problems, always verify that the triangle is indeed right-angled before applying the Pythagorean theorem.