To find the length of the support cable, we can use the Pythagorean theorem, since we have a right triangle formed by the pole, the ground, and the cable.
The vertical side of the triangle is the height at which the cable is attached to the pole (20 ft), and the horizontal side is the distance from the base of the pole to the point where the cable is anchored (10 ft).
Let's denote:
- \( a = 20 \) ft (height of the pole where the cable is attached),
- \( b = 10 \) ft (distance from the base of the pole to the anchor).
The length of the cable, which is the hypotenuse \( c \), can be calculated using the Pythagorean theorem:
\[ c = \sqrt{a^2 + b^2} \]
Substituting in the values:
\[ c = \sqrt{(20)^2 + (10)^2} \] \[ c = \sqrt{400 + 100} \] \[ c = \sqrt{500} \] \[ c = \sqrt{100 \times 5} \] \[ c = 10\sqrt{5} \]
Now, we can calculate \( 10\sqrt{5} \):
Using \( \sqrt{5} \approx 2.236 \):
\[ 10\sqrt{5} \approx 10 \times 2.236 = 22.36 \]
Rounding to the nearest tenth gives:
\[ c \approx 22.4 \text{ ft} \]
Thus, the length of the cable is approximately 22.4 ft.