4. Locating Lost Treasure Whilescuba diving off Wreck Hill in Bermuda, a group o

Question

4. Locating Lost Treasure Whilescuba diving off Wreck Hill in Bermuda, a group of fiveentrepreneurs dis­covered a treasure map in a small watertightcask on a pi­rate schooner that had sunk in 1747. The mapdirected them to an area of Bermuda now known as The Flatts. Thedirections on the map read as follows:

1.        From the tallest palmtree, sight the highest hill. Drop
your eyes vertically until you sight the base of the hill.

2.        Turn 40° clockwisefrom that line and walk 70 paces
to the big red rock.

3.        From the red rock walk50 paces back to the sight line
between the palm tree and the hill. Dig there.

Upon reaching The Flatts, the five entrepreneurs believed that theyhad found the red rock and the highest hill in the vicinity, butthe "tallest palm tree" had long since fallen and disintegrated. Itoccurred to them that the treasure must be located on a circle withradius 50 "paces" centered around the red rock, but they decidedagainst digging a trench 942 feet in circumference, espe­ciallysince they had no assurance that the treasure was still there.(They had decided that a "pace" must be about a yard.)

(a)    Determine a plan to locate the position ofthe lost
palm tree.

(b)    One solution follows: From the location ofthe palm
tree, turn 40° counterclockwise from the rock to the
hill, then go about 50 yards to the circle traced about
the rock. Verify this solution.

(c)          This location did not yield any treasure. Find the other
solution and the treasure. Where is the treasure? How
far is it from the palm tree?

>^rCO

Explanation / Answer

a) So if we draw the triangle with the hill, rock, and palmtree we know one angle and two sides (one is 70 yards and the otheris the distance between the hill and the rock which they shouldknow because they know where the hill and the rock are, since thisis not stated in the problem we will call this: d)

Since we know two sides and an angle we can use the law ofcosines to find the final side and from that find the final twoangles. Now facing the hill from the rock we can turn the appropateabout of degrees and walk the 70 paces to the palm tree.
c) If this location doesn't work it's because the palm tree ison the otherside of the hill than we were thinking about it and theperson should actually turn 40 degrees clockwise!
Sorry that was a little rough, hopefully it helps a bit.

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