To find the length of the cable, we can use the Pythagorean theorem.
In this case, we have a right triangle where:
- One leg is the height from the ground to the attachment point on the pole (20 ft).
- The other leg is the horizontal distance from the base of the pole to the anchor point of the cable (10 ft).
- The hypotenuse is the length of the cable.
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 horizontal distance from the pole (10 ft).
Plugging in the values:
\[ c^2 = 20^2 + 10^2 \] \[ c^2 = 400 + 100 \] \[ c^2 = 500 \] \[ c = \sqrt{500} \] \[ c \approx 22.4 , \text{ft} \]
Therefore, the length of the cable is approximately 22.4 ft.