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. 500 ft. 500 ft. 300 ft. 300 ft. 17.3 ft.

Answer 1

To determine the length of the cable, we can use the Pythagorean theorem. The situation can be visualized as a right triangle where:

- One leg (the vertical leg) is the height from the ground to where the cable is attached to the pole, which is 20 ft.
- The other leg (the horizontal leg) is the distance from the base of the pole to the point where the cable is anchored on the ground, which is 10 ft.
- The hypotenuse represents the length of the cable.

According to the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]

Where:
- \( c \) is the length of the cable,
- \( a \) is the vertical leg (20 ft), and
- \( b \) is the horizontal leg (10 ft).

Now we can substitute the values:
\[ c^2 = 20^2 + 10^2 \]
\[ c^2 = 400 + 100 \]
\[ c^2 = 500 \]

Now, take the square root of both sides to find \( c \):
\[ c = \sqrt{500} \]
\[ c \approx 22.4 \, \text{ft} \]

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