To determine the length of the cable needed to support the volleyball net post, we can use the Pythagorean theorem. The vertical distance from the hook to the ground is 4 ft (the height of the hook), and the horizontal distance from the base of the post to the hook in the floor is 3 ft.
We can represent the vertical and horizontal distances as the two legs of a right triangle, and the length of the cable as the hypotenuse.
Using the Pythagorean theorem:
\[ c = \sqrt{a^2 + b^2} \]
where:
- \( a \) is the vertical distance (4 ft),
- \( b \) is the horizontal distance (3 ft),
- \( c \) is the length of the cable.
Plugging in the values:
\[ c = \sqrt{(4)^2 + (3)^2} \] \[ c = \sqrt{16 + 9} \] \[ c = \sqrt{25} \] \[ c = 5 \text{ ft} \]
So, the length of the cable should be 5 ft.