Question

An electric pole has a support cable that is attached to the pole 20 ft. from the ground. The cable is anchored on the ground 10 ft. from the base of the pole. How long is the cable? Round to the nearest tenth. (1 point)

17.3 ft.

O 22.4 ft.

O 300 ft

O 500 ft.

Answer 1

To find the length of the cable, we can use the Pythagorean theorem. In this scenario, the pole, the ground distance to the cable anchor, and the cable itself form a right triangle.

1. The height of the pole where the cable is attached is \(20\) ft.
2. The distance from the base of the pole to where the cable is anchored is \(10\) ft.

Using the Pythagorean theorem:

\[
c^2 = a^2 + b^2
\]

Where:
- \(c\) is the length of the cable,
- \(a\) is the height of the attachment point (20 ft),
- \(b\) is the distance from the base of the pole to where the cable is anchored (10 ft).

Substituting the given values:

\[
c^2 = 20^2 + 10^2
\]
\[
c^2 = 400 + 100
\]
\[
c^2 = 500
\]
\[
c = \sqrt{500} \approx 22.4
\]

So, the length of the cable, rounded to the nearest tenth, is approximately **22.4 ft**.