Question

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)
Responses

4 ft.
4 ft.

2.65 ft.
2.65 ft.

25 ft.
25 ft.

5 ft.
5 ft.
Remaining Attempts : 3

Answer 1

To find the length of the cable needed to support the volleyball net post, we can visualize the situation as a right triangle.

1. The height of the hook above the court surface is 4 ft (this is one leg of the triangle).
2. The distance from the base of the post to the hook in the floor is 3 ft (this is the other leg of the triangle).

We can use the Pythagorean theorem to calculate the length of the cable, which is the hypotenuse of the right triangle formed by these two legs.

The Pythagorean theorem states that:

\[ a^2 + b^2 = c^2 \]

where \( c \) is the length of the hypotenuse (the cable), and \( a \) and \( b \) are the two other sides.

Here, we have:

- \( a = 4 \) ft (height)
- \( b = 3 \) ft (horizontal distance)

Now plug these values into the formula:

\[ 4^2 + 3^2 = c^2 \]
\[ 16 + 9 = c^2 \]
\[ 25 = c^2 \]
\[ c = \sqrt{25} \]
\[ c = 5 \text{ ft} \]

Therefore, the length of the cable should be **5 ft**.