If a 6 meter pole and a 3 meter pole are connected by wires from the top to bottom, how tall is the pole touching the intersecting wires?

To determine the height of the pole formed by the intersecting wires, we need to use the concept of similar triangles.

First, let's label the poles and the intersecting wires. Let's call the 6-meter pole "Pole A" and the 3-meter pole "Pole B". The pole formed by the intersecting wires will be denoted as "Pole C."

To solve this problem, we can create a proportion using the similar triangles formed by the two poles and the intersecting wires.

Step 1: Set up a proportion:
The height of Pole C can be determined by setting up the proportion between the lengths of Pole A and Pole B compared to the lengths of Pole C and Pole B:

(Pole A) / (Pole B) = (Pole C) / (Pole B)

Step 2: Simplify the proportion:
Since the length of Pole B appears in both the numerator and denominator, it cancels out:

(Pole A) = (Pole C)

Step 3: Substitute the values:
In this case, Pole A has a length of 6 meters, so we can substitute this value into the equation:

6 meters = (Pole C)

Therefore, the height of the pole formed by the intersecting wires is 6 meters.