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

20 ft from the left pole

Step-by-step explanation:

Let x (ft) be the distance from the base of the left pole to the anchor point. Since 2 poles has a distance of 30 ft, the distance from the anchor point to the right pole is 30 - x

The wire length from the top of the left pole to the anchor point is

Similarly for the 2nd part of the wire

We want to minimize the length of the wires, or

we can take the first derivative of this and set it to 0

x = 20