Question

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)
Responses

22.4 ft.
22.4 ft.

17.3 ft.
17.3 ft.

300 ft.
300 ft.

500 ft.

Answer 1

To find the length of the cable, we can use the Pythagorean theorem. In this case, we have a right triangle where:

- One leg of the triangle is the vertical distance from the ground to the attachment point on the pole, which is 20 ft.
- The other leg of the triangle is the horizontal distance from the base of the pole to the anchor point of the cable, which is 10 ft.

Using the Pythagorean theorem, we have:

\[
c = \sqrt{a^2 + b^2}
\]

where \(c\) is the length of the cable, \(a\) is the vertical distance (20 ft), and \(b\) is the horizontal distance (10 ft).

Substituting the values into the formula:

\[
c = \sqrt{(20)^2 + (10)^2}
\]

Calculating the squares:

\[
c = \sqrt{400 + 100}
\]
\[
c = \sqrt{500}
\]
\[
c \approx 22.4 \text{ ft}
\]

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