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)
○ 17.3 ft
○ 500 ft.
○ 300 ft.
○ 22.4 ft

Explanation:

Step1: Identify the triangle type

This is a right triangle problem, where the height of the pole (20 ft) and the distance on the ground (10 ft) are the two legs, and the cable is the hypotenuse. We use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(a = 20\), \(b = 10\), and \(c\) is the cable length.

Step2: Apply the Pythagorean theorem

Substitute the values into the formula: \(c = \sqrt{20^2 + 10^2}\)
Calculate \(20^2 = 400\) and \(10^2 = 100\), so \(c = \sqrt{400 + 100} = \sqrt{500}\)

Step3: Simplify and round

\(\sqrt{500} \approx 22.4\) (rounded to the nearest tenth)

Answer:

22.4 ft