To find the length of the cable, we can use the Pythagorean theorem, which is appropriate in this scenario since we can form a right triangle.
Given:
- The height of the cable attachment on the pole is 20 feet (vertical side).
- The distance from the base of the pole to the anchor point on the ground is 10 feet (horizontal side).
Let's denote the length of the cable as \( c \). According to the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
where:
- \( a \) is the height of the attachment (20 feet),
- \( b \) is the horizontal distance to the anchor (10 feet).
So,
\[ c^2 = 20^2 + 10^2 \]
Calculating each term:
\[ 20^2 = 400 \] \[ 10^2 = 100 \]
Adding these:
\[ c^2 = 400 + 100 = 500 \]
Now, taking the square root to find \( c \):
\[ c = \sqrt{500} \approx 22.36 \text{ feet} \]
Rounding to the nearest tenth:
\[ c \approx 22.4 \text{ feet} \]
Thus, the length of the cable is approximately 22.4 feet.