Final answer:
The correct equation to find the distance Joe has climbed up the ladder is C. 3.2² + 2.4² = c², which is based on the Pythagorean theorem.
Step-by-step explanation:
The situation described involves Joe stopping on a ladder with his feet vertically 3.2 feet above the ground and horizontally 2.4 feet from the base of the ladder. The equation that represents this scenario is based on the Pythagorean theorem, which applies to right triangles. Since the ladder, the ground, and the line from Joe's feet to the base of the ladder form a right triangle, we can use the theorem to find the length of the ladder Joe has climbed, which is the hypotenuse of the triangle.
The correct equation to represent this new situation is:
C. 3.2² + 2.4² = c²
This equation states that the square of the height of the ladder above the ground (3.2²) plus the square of the horizontal distance from the base of the ladder to Joe's feet (2.4²) equals the square of the distance Joe has climbed the ladder (c²).