To find the length of the cable, we can use the Pythagorean theorem, which applies to right triangles. In this case, we have a right triangle formed by:
- The height of the pole (20 ft), which is one leg of the triangle.
- The distance from the base of the pole to the anchor point of the cable (10 ft), which is the other leg of the triangle.
- The cable itself, which forms the hypotenuse.
Using the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
where \(a\) and \(b\) are the legs of the triangle, and \(c\) is the hypotenuse.
Here, \(a = 20\) ft and \(b = 10\) ft. We want to find \(c\):
\[ 20^2 + 10^2 = c^2 \]
Calculating the squares:
\[ 400 + 100 = c^2 \] \[ 500 = c^2 \]
Now, we take the square root of both sides to find \(c\):
\[ c = \sqrt{500} \approx 22.36 \]
Rounding to the nearest tenth, we get:
\[ c \approx 22.4 \text{ ft.} \]
Thus, the length of the cable is approximately 22.4 ft.