To find the length of the support cable, we can use the Pythagorean theorem. The situation describes a right triangle where:
- One leg (the height of the pole where the cable is attached) is 20 ft.
- The other leg (the horizontal distance from the base of the pole to where the cable is anchored) is 10 ft.
- The cable itself forms the hypotenuse of the triangle.
Using the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
where:
- \(c\) is the length of the cable (hypotenuse),
- \(a\) is the height of the pole (20 ft),
- \(b\) is the distance from the pole to the anchor (10 ft).
Substituting the values into the equation:
\[ c^2 = 20^2 + 10^2 \] \[ c^2 = 400 + 100 \] \[ c^2 = 500 \] \[ c = \sqrt{500} \] \[ c \approx 22.36 \]
Rounding to the nearest tenth, the length of the support cable is approximately 22.4 ft.
The correct answer is 22.4 ft.