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. The setup can be visualized as a right triangle, where:

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

Using the Pythagorean theorem, which states that \( a^2 + b^2 = c^2 \) (where \( c \) is the hypotenuse), we can substitute the values into the equation:

\[
a = 20 \, \text{ft} \\
b = 10 \, \text{ft}
\]

Calculating:

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

\[
400 + 100 = c^2
\]

\[
500 = c^2
\]

Now taking the square root to find \( c \):

\[
c = \sqrt{500} \approx 22.36 \, \text{ft}
\]

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

So the correct answer is **22.4 ft**.