To determine the length of the cable, we can use the Pythagorean theorem. The height of the hook above the court surface is 4 feet, and the horizontal distance from the base of the post to the hook in the floor is 3 feet.
We can visualize this as a right triangle where:
- One leg (the height) is 4 feet,
- The other leg (the horizontal distance) is 3 feet,
- The hypotenuse (the length of the cable) is what we need to find.
According to the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
Where:
- \(c\) is the hypotenuse,
- \(a\) is one leg (4 feet),
- \(b\) is the other leg (3 feet).
Plugging in the values:
\[ c^2 = 4^2 + 3^2 \] \[ c^2 = 16 + 9 \] \[ c^2 = 25 \] \[ c = \sqrt{25} \] \[ c = 5 \]
Therefore, the length of the cable should be 5 ft.