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. 300 ft. 300 ft. 500 ft. 500 ft. 17.3 ft.

Answer 1

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

- The height from the ground to where the cable is attached to the pole is \(20\) ft.
- The distance from the base of the pole to where the cable is anchored on the ground is \(10\) ft.
- The cable itself is the hypotenuse of the triangle.

According to the Pythagorean theorem:

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

where:
- \(c\) is the length of the cable,
- \(a\) is the height of the pole (20 ft),
- \(b\) is the distance from the pole to the anchor point on the ground (10 ft).

Now, we can substitute the values into the equation:

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

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