To find the length of the cable, we can use the Pythagorean theorem. The situation can be visualized as a right triangle where:
- One leg is the height of the pole at which the cable is attached (20 ft).
- The other leg is the horizontal distance from the base of the pole to the point where the cable is anchored (10 ft).
- The cable, which is the hypotenuse of the triangle, is what we want to find.
Using the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
where:
- \( c \) is the length of the cable,
- \( a \) is the height of the cable attachment (20 ft),
- \( b \) is the distance from the base of the pole to the anchor point (10 ft).
Substituting the values in:
\[ c^2 = 20^2 + 10^2 \] \[ c^2 = 400 + 100 \] \[ c^2 = 500 \] \[ c = \sqrt{500} \] \[ c \approx 22.4 \text{ ft} \]
Therefore, the length of the cable is approximately 22.4 ft.