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.

500 ft.
500 ft.

17.3 ft.
17.3 ft.

300 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 is the height from the ground to the attachment point on the pole (20 ft).
- The other leg is the horizontal distance from the base of the pole to the anchor point of the cable (10 ft).
- The hypotenuse is the length of the cable.

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 horizontal distance from the pole (10 ft).

Plugging in the values:

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

Therefore, the length of the cable is approximately **22.4 ft.**