Problem:
A young man was going through the attic of his grandfather's house and found a paper describing the location of a buried treasure on a particular Island. The note said that on the island one would find a gallows, an oak tree, and a pine tree. To locate the treasure one would begin at the gallows, walk to the pine tree, turn right 90 degrees and walk the same number of paces away from the pine tree. A spike was to be driven at that point. Then return to the gallows, walk to the oak tree and turn left 90 degrees and walk the same number of paces away from the oak tree. Drive a second spike in the ground. The midpoint of a string drawn between the two spikes would locate the treasure.
The young man and his friends mounted an expedition to the island but found the oak tree and the pine tree but no gallows. Their boat was swept out to sea, leaving them stranded. They knew that the "treasure" also contained certain items that would be essential to their survival.
Show them where to look for the treasure.
Here is a map of the island.
What are we going to do? Since we don't know where the gallows were located, let's pick a spot for them and see what happens. I have used Geometer's Sketchpad to illustrate the situation.
Explore the problem. When you come to a conclusion, prove it!
Please e-mail me with your findings. Have fun!!