To determine the length of the cable needed to support the volleyball net post, we can visualize the scenario as a right triangle where the height difference and the horizontal distance are the two legs of the triangle.
- Height of the hook above the court surface: 4 ft (vertical leg).
- Distance from the base of the post to the hook in the floor: 3 ft (horizontal leg).
We can use the Pythagorean theorem to find the length of the cable, which acts as the hypotenuse of the right triangle. The Pythagorean theorem states:
\[ c^2 = a^2 + b^2 \]
Where:
- \(c\) is the length of the cable,
- \(a\) is the vertical leg (4 ft),
- \(b\) is the horizontal leg (3 ft).
Calculating the squares of the legs:
\[ 4^2 = 16 \] \[ 3^2 = 9 \]
Now, add these values:
\[ c^2 = 16 + 9 = 25 \]
Next, take the square root of both sides to find \(c\):
\[ c = \sqrt{25} = 5 \]
Thus, the length of the cable should be 5 feet.