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Chapter 23: Problem 57

One strategy for identifying a central location is called triangulation. In triangulation, a central position can be pinpointed by knowing the distance from each of three different places. First, on a piece of paper, create a rough map showing where each person in your group lives. Second, create a circle around each person's home that has a radius equal to the distance that each home is from your classroom. Label the place where the circles intersect as your classroom. Why can you not identify the position of the classroom with only two people's circles?

Short Answer

Expert verified
Two people's circles will have two possible intersection points, therefore we can't accurately pinpoint a single location. We need at least three people's circles (triangulation) to locate the classroom.

Step by step solution

01

Understanding Triangulation Concept

Triangulation is a method used in geometry to determine a specific point by measuring angles to it from known points at either end of a fixed baseline. To apply the concept of triangulation, we need at least three different points. If we consider each person's home as a point, then we need at least three homes or people for effective triangulation.
02

Understanding Circles Interaction

The drawn circles around each person's home represent the maximum distance each person is from the classroom. If only two circles are considered, there are two possible points of intersection, hence it is not possible to accurately pinpoint the location of the classroom. On the other hand, when three circles are considered, they normally intersect at a single point, allowing us to locate the classroom.
03

Conclusion

Thus, two people's circles are not enough to identify the classroom position as they create an area of uncertainty with two possible intersection points. We need at least three people's circles for triangulation, as the intersection of the three circles should result in one point which would be the central position - in this case the classroom.

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