Geometry Pirate Treasure Problem

[johnkid]

My teacher assigned this very confusing, at least to me, problem.

(Summed up by me.): Some people found a treasure map, authenticated it and now looking for it. Here's what it says:

"Start from the tree, walk directly to the falcon-shaped rock. Count your paces as you walk. Turn a quarter-circle to the right and walk the same number of paces. When you reach the end put a stick in the ground. Return to the tree and likewise walk to the owl-shaped rock, again counting your paces. Turn a quarter-circle to the left, walk the same number of paces, and put another stick in the ground. Connect the two sticks with a rope. The treasure is beneath the midpoint of the rope."

HOWEVER, the tree was no longer on the island. All that was left was the two weird shaped rocks. The people gave up looking for the treasure.

Did the people give up too soon? Is it possible to find the treasure without the tree? Explain and give a rough sketch.




My answer is no. I think there are way to many possiblities. If the rocks change positions, there are even more possiblities. I drew out a lot of sketches and my head starts to hurt. So, if you know of the answers would you please explain it to me? Thanks

 

[Deleted member 4993]

Some people found a treasure map, authenticated it and now looking for it. Here's what it says:

"Start from the tree, walk directly to the falcon-shaped rock. Count your paces as you walk. Turn a quarter-circle to the right and walk the same number of paces. When you reach the end put a stick in the ground. Return to the tree and likewise walk to the owl-shaped rock, again counting your paces. Turn a quarter-circle to the left, walk the same number of paces, and put another stick in the ground. Connect the two sticks with a rope. The treasure is beneath the midpoint of the rope."

HOWEVER, the tree was no longer on the island. All that was left was the two weird shaped rocks. The people gave up looking for the treasure.

Did the people give up too soon? Is it possible to find the treasure without the tree? Explain and give a rough sketch.

What type of math are you in?

You can solve this problem by using "imaginary" numbers. Look into the book by George Gammow - "One, Two, Three...infinity". It is solved in there.

 

[TchrWill]

My teacher assigned this very confusing, at least to me, problem.

(Summed up by me.): Some people found a treasure map, authenticated it and now looking for it. Here's what it says:

"Start from the tree, walk directly to the falcon-shaped rock. Count your paces as you walk. Turn a quarter-circle to the right and walk the same number of paces. When you reach the end put a stick in the ground. Return to the tree and likewise walk to the owl-shaped rock, again counting your paces. Turn a quarter-circle to the left, walk the same number of paces, and put another stick in the ground. Connect the two sticks with a rope. The treasure is beneath the midpoint of the rope."

HOWEVER, the tree was no longer on the island. All that was left was the two weird shaped rocks. The people gave up looking for the treasure.

Did the people give up too soon? Is it possible to find the treasure without the tree? Explain and give a rough sketch.

My answer is no. I think there are way to many possiblities. If the rocks change positions, there are even more possiblities. I drew out a lot of sketches and my head starts to hurt. So, if you know of the answers would you please explain it to me? Thanks

The following skighty different version of the same type of problem should convince you that there is a solution.

1/16/02

Two rocks are 100ft apart. A palm tree is somewhere between the two rocks and about 80ft from them, and at the edge of the water. From each rock I sighted the palm tree and marked the line segment from the rock to the palm tree, then rotated the segment by 90 degrees away from the palm tree and the other rock. I then marked the endpoints of the rotated line segments on the ground. I buried the treasure half way between those two endpoints. A yr. later, two rocks are still there, but the palm tree is cut off. Where is the treasure?

First, the all important figure:
1--Draw a horizontal line representing the shoreline.
2--Locate a point C on the shoreline representing the palm tree.
3--Draw a line ~80 ft. long at ~55º to the shore, upward to the left, the end point representing the first rock, A.
4--Draw a line ~80 ft. long at ~50º to the shore, upward to the right, the end point representing the second rock, B. (Distance AB = 100 ft.)
5--With radius BC and B as center, swing a 90º arc calling the new location of point C, point E.
6--With radius AC and A as center, swing a 90º arc calling the new location of point C, point F.
7--Draw line EF.
8--Bisect EF calling the mid point T.
9--Drop perpendiculars to AB from C, E, F, and T.
10--Label the intersections on AB as G from point E, D from point C, H from point F, and J from point T.
11--/_ACD = /_FAD
12--Therefore, FH = AD
13--/_DCB = /_EBG
14--Therefore, EG = DB
15--TJ = (EG + FH)/2
16--Therefore, TJ equals half the distance between the rocks.
17--AH = GB = CD
18--GD = DH
19--Therefore, AD = DB and D is the mid point of AB, the distance between the two rocks.
20--Thus, upon returning to the site and finding the palm tree gone, one need only construct a perpendicular to the line AB, the line joining the two rocks, at the mid point of AB, 50 ft. from either A or B, and pace off a distance equal to 50 ft. away from the shoreline to locate the treasure.