Two poles are connected by a wire that is also connected to the ground. the first pole is 20ft tall and the second pole is 10ft tall. there is a distance of 30ft between the two poles. where should the wire be anchored to the ground to minimize the amount of wire needed

31.6ft

Explanation:

Check the attachment for the diagram.

According to the right angle triangle AEC, we will use Pythagoras theorem to get |AC|. Note that |AE| = |AB| - |CD|

that is 20ft - 10ft = 10ft

According to the theorem, the square of the sum of the adjacent side and the opposite side is equal to the square of the hypotenuse.

|AE|^2 + |EC|^2 = |AC|^2

10^2 + 30^2 = |AC|^2

100 + 900 = |AC|^2

|AC| = √1000

|AC| = 31.6ft

Therefore, the wire should be anchored 31.6ft to the ground to minimize the amount of wire needed.

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