What is the distance between the tops of two poles, one 6m tall and the other 11m tall, located 12m apart on level ground?

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To find the distance between the tops of the two poles, we can use the distance formula derived from the Pythagorean theorem. The two poles can be visualized as forming a right triangle with the ground.

Let’s break down the problem:

  1. **Height of the first pole**: 6 meters
  2. **Height of the second pole**: 11 meters
  3. **Horizontal distance between the bases of the poles**: 12 meters

First, we calculate the vertical distance between the tops of the two poles:

  • **Vertical distance** = Height of the second pole – Height of the first pole = 11m – 6m = 5m

Now, we have a right triangle where:

  • One leg is the vertical distance (5m)
  • The other leg is the horizontal distance (12m)

Using the Pythagorean theorem:

a² + b² = c²

Where:

  • a = horizontal distance = 12m
  • b = vertical distance = 5m
  • c = distance between the tops of the poles

Substituting the values:

(12)² + (5)² = c²

This simplifies to:

144 + 25 = c²

Thus:

169 = c²

Now, taking the square root of both sides gives:

c = √169

Therefore, the distance between the tops of the two poles is:

c = 13m

In conclusion, the distance between the tops of the two poles, situated 12 meters apart on level ground, is 13 meters.

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