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

300 ft.
300 ft.

22.4 ft.
22.4 ft.

500 ft.
500 ft.

17.3 ft.

Answer 1

To find the length of the cable, we can use the Pythagorean theorem, which applies to right triangles. In this case, we have a right triangle formed by:

- The height of the pole (20 ft), which is one leg of the triangle.
- The distance from the base of the pole to the anchor point of the cable (10 ft), which is the other leg of the triangle.
- The cable itself, which forms the hypotenuse.

Using the Pythagorean theorem:

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

where \(a\) and \(b\) are the legs of the triangle, and \(c\) is the hypotenuse.

Here, \(a = 20\) ft and \(b = 10\) ft. We want to find \(c\):

\[
20^2 + 10^2 = c^2
\]

Calculating the squares:

\[
400 + 100 = c^2
\]
\[
500 = c^2
\]

Now, we take the square root of both sides to find \(c\):

\[
c = \sqrt{500} \approx 22.36
\]

Rounding to the nearest tenth, we get:

\[
c \approx 22.4 \text{ ft.}
\]

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