Question

use the pythagorean theorem quick check
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)
500 ft.
17.3 ft.
300 ft.
22.4 ft.

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 20\) (height of attachment on pole), \(b=10\) (distance from base on ground), and \(c\) is the length of the cable.
So, \(c^{2}=20^{2}+10^{2}\).

Step2: Calculate \(c^{2}\)

\(20^{2}=400\), \(10^{2} = 100\). Then \(c^{2}=400 + 100=500\).

Step3: Find \(c\)

\(c=\sqrt{500}\approx22.4\) (rounded to the nearest tenth).

Answer:

22.4 ft.