Final answer:
To find the length of the third side of a right triangle, we can use the Pythagorean theorem. In this case, the length of the third side is 9 m.
Step-by-step explanation:
To find the length of the third side of a right triangle, we can use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. In this case, we have the length of one leg (12 m) and the length of the hypotenuse (15 m). Let's call the length of the other leg x.
Using the Pythagorean theorem, we have 12² + x² = 15². Simplifying this equation, we get 144 + x² = 225. Subtracting 144 from both sides, we get x² = 81. Taking the square root of both sides, we find that x = 9.
The length of the third side of the right triangle is 9 m. Therefore, the correct answer is C. 9 m.