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?