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)

Answer 1

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

- One leg of the triangle is the vertical distance from the court surface to the hook on the post (4 ft).
- The other leg is the horizontal distance from the base of the post to the hook in the floor (3 ft).

We can use the Pythagorean theorem to find the length of the cable, which is the hypotenuse of the triangle. The Pythagorean theorem states:

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

Where:
- \( c \) is the length of the cable.
- \( a \) is the vertical distance (4 ft).
- \( b \) is the horizontal distance (3 ft).

Plugging in the values:

\[
c^2 = 4^2 + 3^2
\]
\[
c^2 = 16 + 9
\]
\[
c^2 = 25
\]

Taking the square root of both sides gives:

\[
c = \sqrt{25}
\]
\[
c = 5 \text{ ft}
\]

Thus, the length of the cable should be **5 feet**.