Find the Distance Between Two Water Towers – Orienteering

In this case I have not actually tried out my measurements in the video to see if they are even close to the actual answer, because when I do this problem the students take their own measurements with their smartphones.   That includes headings and distances.   There are some real rough estimates here, but some great mathematics.   This video is just an example of the set up.  I take my students on a bus out in the country to do this problem.  I split them into groups of 2 or 3, and told them that whomever can prove their answer the closest with the measurements they collect will be the orienteering champions.  Since roads all follow north, south, east, west lines.  It is easy to take heading measurement in one location to two distant objects.  Drive East a certain distance get out and take the measurements again.  For instance in the image  below we took 6 measurements.  The headings to each tack at each endpoint of the red and blue lines.

The red and blue line segments are exactly one mile. We took headings at each endpoint and created two problems. With these measurements it is possible to find the distance between the two thumb tacks.

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