While scuba diving off Wreck Hill in Bermuda, group of 5 entrepreneurs discovered treasure map in small watertight cask on pirate schooner which had sunk in 1747. Map directed them to the area of Bermuda now known as The Flatts.
Directions on map read as follows.
1. From tallest palm tree, sight highest hill. Drop the eyes vertically until you sight base of the hill.
2. Turn 40° clockwise from that line and walk 70 paces to big red rock.
3. From red rock walk 50 paces back to sight line between palm tree and hill. Dig there.
Upon reaching The Flatts, 5 entrepreneurs thought that they had found red rock and highest hill in vicinity, but "tallest palm tree" had long since fallen and disintegrated. It happened to them that treasure should be located on circle with radius 50 "paces" centered around red rock, but they made decision against digging trench 942 feet in circumference, particularly since they had no assurance that treasure was still there. (They decided that "pace" should be about a yard.)
a) Find plan to locate position of the lost palm tree.
b) Entrepreneur with most math background comes up with solution: From location of palm tree, turn 40° counterclockwise from rock to hill, then go about 50 yards to circle traced about rock. Is this possible solution? Why or Why not? Support answer mathematically.
c) Location didn't yield any treasure. Determine other solution and treasure. Where is treasure? How far is it from the palm tree?