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

300 ft.
300 ft.

500 ft.
500 ft.

17.3 ft.
17.3 ft.

22.4 ft.

Answer 1

To find the length of the cable, we can use the Pythagorean theorem. The problem gives us a right triangle where:

• The height of the pole creates one leg of the triangle (20 ft).
• The distance from the base of the pole to the anchor point on the ground creates the other leg of the triangle (10 ft).
• The cable itself is the hypotenuse of the triangle.

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

\[ c^2 = \text{(height)}^2 + \text{(distance from the pole)}^2 \]

Substituting the values:

\[ c^2 = (20)^2 + (10)^2 \] \[ c^2 = 400 + 100 \] \[ c^2 = 500 \] \[ c = \sqrt{500} \approx 22.36 \]

Rounding this to the nearest tenth, we get:

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

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