A volleyball net post needs a cable to support it. The hook to attach the cable is 4 ft. above the court surface, and the hook in the floor is 3 ft. from the base of the post. How long should the cable be?(1 point)

Question

Responses

25 ft.
25 ft.

4 ft.
4 ft.

5 ft.
5 ft.

2.65 ft.

Answer 1

To find the length of the cable needed to support the volleyball net post, we can use the Pythagorean theorem.

1. The vertical distance from the hook above the court surface to the floor is 4 ft.
2. The horizontal distance from the post to the hook in the floor is 3 ft.

You can visualize this situation as a right triangle, where:

• One leg (vertical) is 4 ft,
• The other leg (horizontal) is 3 ft,
• The length of the cable (hypotenuse) is what we need to find.

Using the Pythagorean theorem: \[ c^2 = a^2 + b^2 \] Where:

• \(c\) is the length of the cable,
• \(a\) is the vertical distance,
• \(b\) is the horizontal distance.

Substituting the values: \[ c^2 = (4 , ft)^2 + (3 , ft)^2 \] \[ c^2 = 16 , ft^2 + 9 , ft^2 \] \[ c^2 = 25 , ft^2 \] \[ c = \sqrt{25 , ft^2} = 5 , ft \]

Thus, the length of the cable should be 5 ft.

The correct response is: 5 ft.