Question

an electric pole has a support cable that is attached to the pole 20ft from the ground the cable is anchored on the ground 10 ft drom the base of the pole how long is the cable round to the nearth tenth

Answer 1

To find the length of the cable, we can use the Pythagorean theorem, which is appropriate in this scenario since we can form a right triangle.

Given:
- The height of the cable attachment on the pole is 20 feet (vertical side).
- The distance from the base of the pole to the anchor point on the ground is 10 feet (horizontal side).

Let's denote the length of the cable as \( c \). According to the Pythagorean theorem:

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

where:
- \( a \) is the height of the attachment (20 feet),
- \( b \) is the horizontal distance to the anchor (10 feet).

So,

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

Calculating each term:

\[
20^2 = 400
\]
\[
10^2 = 100
\]

Adding these:

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

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

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

Rounding to the nearest tenth:

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

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