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

Answer 1

To find the length of the support cable, we can use the Pythagorean theorem, since we have a right triangle formed by the pole, the ground, and the cable.

The vertical side of the triangle is the height at which the cable is attached to the pole (20 ft), and the horizontal side is the distance from the base of the pole to the point where the cable is anchored (10 ft).

Let's denote:
- \( a = 20 \) ft (height of the pole where the cable is attached),
- \( b = 10 \) ft (distance from the base of the pole to the anchor).

The length of the cable, which is the hypotenuse \( c \), can be calculated using the Pythagorean theorem:

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

Substituting in the values:

\[
c = \sqrt{(20)^2 + (10)^2}
\]
\[
c = \sqrt{400 + 100}
\]
\[
c = \sqrt{500}
\]
\[
c = \sqrt{100 \times 5}
\]
\[
c = 10\sqrt{5}
\]

Now, we can calculate \( 10\sqrt{5} \):

Using \( \sqrt{5} \approx 2.236 \):

\[
10\sqrt{5} \approx 10 \times 2.236 = 22.36
\]

Rounding to the nearest tenth gives:

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

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