To find the length of the cable, we can use the Pythagorean theorem. In this scenario, the pole, the ground distance to the cable anchor, and the cable itself form a right triangle.
- The height of the pole where the cable is attached is \(20\) ft.
- The distance from the base of the pole to where the cable is anchored is \(10\) ft.
Using the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
Where:
- \(c\) is the length of the cable,
- \(a\) is the height of the attachment point (20 ft),
- \(b\) is the distance from the base of the pole to where the cable is anchored (10 ft).
Substituting the given values:
\[ c^2 = 20^2 + 10^2 \] \[ c^2 = 400 + 100 \] \[ c^2 = 500 \] \[ c = \sqrt{500} \approx 22.4 \]
So, the length of the cable, rounded to the nearest tenth, is approximately 22.4 ft.