Buried Treasure
Name
Captain Coldhart of the pirate ship Xavier always buries his treasures on Deadman’s Island. Use
the maps of the island provided (on the other sheets) to find the locations of his buried
treasures.
1.) Pirate Alphonse is standing at the edge of Westend Bay (at point A), and his cohort, pirate
Beaumont, is 60 paces to the north at point B. Each pirate can see Captain Coldhart off
in an easterly direction, burying treasure. With his sextant, Alphonse measures the angle
between the captain and Beaumont and finds that it measures 85°. With his sextant,
Beaumont measures the angle between the captain and Alphonse and finds that it
measures 48°. Alphonse and Beaumont mark their positions with large boulders and return
to their ship, confident that they have enough information to return later and recover the
treasure.
Use your geometry tools to locate all possible locations for the treasure and mark it/them
with an X on Map 1.
Can they recover the treasure by digging a single hole? Yes
/
No
If they do not have enough information, explain why not. How many possible locations for
the treasure are there?
2.) Captain Coldhart, convinced that someone in his crew stole his last treasure, has decided
to be more careful about burying his current loot. He gives his trusted first mate, Dexter,
two ropes, the lengths of which only the captain knows. The captain instructs Dexter to
nail one end of the shorter rope to Hangman’s Tree (at point H ) and to secure the longer
rope through the eyes of Skull Rock (at point S ). The captain, with the ends of the two
ropes in one hand and the treasure chest tucked under the other arm, walks away from
the shore to the point where the two ropes become taut. He buries the treasure at the
point where the two ropes come together, collects his ropes, and returns confidently to
the ship. The two ropes are respectively 100 paces and 150 paces in length.
Use your geometry tools to find all possible treasure locations on Map 2.
Can the captain recover the treasure by digging a single hole? Yes
/
No
If he does not have enough information, explain why not. How many possible locations for
the treasure are there?
3.) After the theft of two very important ropes from his locker and the subsequent
disappearance of his trusted first mate, Dexter, Captain Coldhart is determined that no
one will find the location of his latest buried treasure. The captain, with his new first
mate, Endersby, walks out to Deadman’s Point (at point D). The captain instructs his first
mate to walk inland along a straight path for a distance of 130 paces. There, Endersby is
to drive his sword into the ground for a marker (at point M ), turn and face in the direction
of the captain, turn at an arbitrary angle to the left, continue to walk for another 60 paces,
stop, and wait for the captain. The captain measures the angle formed by the lines from
Endersby to himself and from himself to the sword. The angle measures 26°. The captain
places a boulder where he is standing (at point D), walks around the bay to Endersby, and
instructs him to bury the treasure at this point.
Use your geometry tools to find all possible treasure locations on Map 3.
Can the captain recover the treasure by digging a single hole? Yes
/
No
If he does not have enough information, explain why not. How many possible locations for
the treasure are there?
4.) Captain Coldhart decides to make one last attempt to bury his treasure in a single secret
location. He walks from point A to point M, turns eastward so that he creates a 50° angle from
point A, and then walks 40 more paces.
Use your geometry tools to find all possible treasure locations on Map 4.
Can the captain recover the treasure by digging a single hole? Yes
/
No
If he does not have enough information, explain why not. How many possible locations for
the treasure are there?
Map One
Map Two
Map Three
Map Four