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 that supports the volleyball net post, we can use the Pythagorean theorem.

We have a right triangle where:

• One leg (the height from the floor to the hook above the court) is 4 ft.
• The other leg (the horizontal distance from the base of the post to the hook in the floor) is 3 ft.

Let \( c \) be the length of the cable (the hypotenuse of the triangle). According to the Pythagorean theorem:

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

where \( a = 4 \) ft (the vertical distance) and \( b = 3 \) ft (the horizontal distance).

Substituting the values in:

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

Taking the square root of both sides to find \( c \):

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

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