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)

Question

Responses

22.4 ft.
22.4 ft.

300 ft.
300 ft.

500 ft.
500 ft.

17.3 ft.

Answer 1

To determine the length of the cable, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case:

• One side (the height of the pole where the cable is attached) is 20 ft.
• The other side (the distance from the base of the pole to where the cable is anchored) is 10 ft.

Let $c$ be the length of the cable (the hypotenuse). According to the Pythagorean theorem:

$$c^2=a^2+b^2$$ where $a=20$ ft and $b=10$ ft.

Now substituting the values:

$$c^2={20}^2+{10}^2$$ $$c^2=400+100$$ $$c^2=500$$

Taking the square root to find $c$:

$$c=\sqrt{500}\approx 22.36$$

Rounding to the nearest tenth, we find that:

$$c\approx 22.4\text{ ft.}$$

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