Triangles Triangles Everywhere¹

-Letterboxer's Version-

Note to KMLHS and future KMLHS students:  Do not go find these letterboxes until you are assigned to in Trigonometry or PreCalc class.  These clues are for regular letterboxers – NOT for students.  When it is assigned, you can click on the following link to print off a copy: student version

Materials Needed: Normal supplies plus maybe a pencil, protractor, and scientific calculator.  There should be a protractor in the first two boxes.
 

Please use wet and dry rags to clean the stamps when you are done stamping up so there is no mess left for the next person that finds the box.  This is particularly important for these boxes as some of the stamps are multi-colored and inking pens are provided, and I want to preserve the coloring.  (Note: Inking pens are included in the boxes for this purpose.)

As you find the boxes, you will need to pick up the next “letterboxer version” clue sheet which you will find in the “letterboxers” baggies in the boxes.  Since there are “regular letterboxer” (blue) and “student version” (white) clue sheets in the boxes, be sure to pick up the correct one.

Letterboxers are more than welcome to try out or check out the student version of the clues.  Do note that the student version requires more than your usual letterboxing materials.  In particular, the students take a “kit” which has the following: the student version of the clues, plastic sheet protector, compass, protractor with straw attached to bottom and a plumb line connected to the center hole (the surveying device), small tape measure (25 ft), large “chalkboard” protractor, regular protractor, clip board, inking pens/ink pad, and wet and dry rags in baggies.  In addition they bring: Pencil/pen, camera (digital preferred), rubber stamp, watch (with seconds), graphics calculator, your textbook and notes.  (Maybe take sand shovels and pails for you sand castle?)  Some like taking a blanket or folding chair to sit on while “stamping up”.  None of the "extra" activities in the student version have anything to do with finding the actual boxes - they are just activities for the students to apply their trigonometry along the way!

Enjoy!

Letterboxers may want to print off information on coordinate planes and quadrants, reference angles and angles in “standard position” before attempting this series of boxes.

Note: The clues to the next box are in the previous box except for Box 1.
 

Triangles! Triangles! Everywhere! Letterboxes

Student Clue Sheet #1

Traveling to Regner Park
 

Drive to the intersection of County P and Hwy 60 in Jackson (just east of the Hwy 60 exit from Hwy 45).  Drive north on County P to West Bend where it becomes Main St.  Along the way, you should be able to spot many examples of how triangles are used just traveling down the road.
 

Regner Park

Travel north on Main St. (Hwy P) through West Bend past HWY 33 (you’ll have to go around “downtown” West Bend) to Park Rd., then take Park Rd. west (left).  Park your car in the Regner Park parking lot with the entrance at 10th and Park.  Park on the west side of the lot.

The first thing to notice after getting out of the car is the gray electrical meter with a wooden backing.  Go to the green electrical box a few feet away.  On top is a number ( __ __ __ ) with “WBSC”.  Add the three digits to get the value of A = ______. (You’ll need info recorded like this later on.)  Look on the back side for the seven digit serial number for this box __ __ __ - __ __ __ __ .  Make the first three numbers form a three digit number ( _____ ), the next two digits form a two digit number ( ____ ), and the last two digits form another two digit number ( ____ ).  Add these three new numbers together to get the value of B = _______.

 

Walk west along the paved path to the bandstand area.  Look at the roofs on these buildings!  What are they made up of?!

 

The middle building was presented to West Bend by the fire department in what year? _______
Take the first three digits as a three digit number and subtract the last digit twice to get the value of C = ______.

 

The bandstand is an interesting shape!  How many sides does it have? ______  Multiply this number by 0.4 to get the value of D = ______.

 

Hey!  There’s another one of those big green electrical boxes to the east of the bandstand.
What is the yellow serial number on it?  __  __  __ - __ __ __ __

Take the first three digits as a three digit number and add each of the four remaining individual digits to get the value of E = ______.

 

Fire!  Rush to the closest fire hydrant!
Oh! But it may be too old!  What year is on the hydrant? ______  Take the first three digits as a three digit number and subtract the last digit to get the value of F = ______.

Fire’s out!  Time to play!  Walk to the playgrounds to the west.  On your way, you’ll pass through a picnic area with a blue drinking fountain (bubbler) to the west of the bandstand.  Record the number of the picnic area as G = _______.

(Here’s a fun student activity you might try to practice your compass skills.  You can skip it if you’d like)

Playing in the Sand:

Walk to the beach that is nearby to the south.
Place yourself in the middle of a flat part of the beach so you have lots of room to move.

Face yourself at a bearing of 210 degrees.

Take 10 baby steps (heel to toe) in that direction.

(With each step, cut a path in the sand with your foot).

Turn 60 degrees to the right and sight the new bearing of __________ degrees.

Walk 10 baby steps in that direction.

Turn 120 degrees to the left and sight the new bearing of __________ degrees.

Walk another 10 baby steps in that direction.

Turn 60 degrees to the right and sight the new bearing of __________ degrees.

Walk another 10 baby steps in that direction.

Turn 120 degrees to the left and sight the new bearing of __________ degrees.

Walk another 10 baby steps in that direction.

Turn 60 degrees to the right and sight the new bearing of __________ degrees.

Walk another 10 baby steps in that direction.

Turn 120 degrees to the left and sight the new bearing of __________ degrees.

Walk another 10 baby steps in that direction.

Turn 60 degrees to the right and sight the new bearing of __________ degrees.

Walk another 10 baby steps in that direction.

Turn 120 degrees to the left and sight the new bearing of (-)______ / (+)______ degrees.

(Ah! You have to find the positive co-terminal angle!)
Walk another 10 baby steps in that direction.

Turn 60 degrees to the right and sight the new bearing of __________ degrees.

Walk another 10 baby steps in that direction.

Turn 120 degrees to the left and sight the new bearing of (-)______ / (+)______ degrees.

(Ah! You have to find the positive co-terminal angle!)
Walk another 10 baby steps in that direction.

Turn 60 degrees to the right and sight the new bearing of (-)______ / (+)______ degrees.

(Ah! You have to find the positive co-terminal angle!)
Walk another 10 baby steps in that direction.

You should now be back at the beginning.

What shape did you form (be specific) ? ___________

Build a sand castle in the middle! Don’t forget to take a picture! J

Finding Box 1 - Sierpinski’s Triangle:

When you’re in the playground area, find the three benches that form a square ((?!) well, sort of).  Stand on the south side of the tree that is just east of these benches.

Now take a bearing of C _____ degrees.  (Remember, I told you you’d need those answers!)  Look in the distance on that bearing for a way to climb a mountain (ok, large hill).  Go climb the hill!

BTW, on the way, you might walk across a cement area that has square designs cut into the concrete.  However, some of the squares are incomplete at the edges, etc. so there are more shapes than just the squares – including triangles!  Can you count the number of triangles formed in the concrete? (This number is not used later.)

As you climb the hill, there are objects made of a natural material that are there to assist your assent (and prevent erosion).  Count the number of these objects as you make your way to the top: H = _______

At the top stop and catch your breath.  You’ll notice there are two ways to go now.  Take the path at a bearing of E ______ degrees.  (You might want to remember the other direction as a way to get back to your car when you’re done at Regner Park.)

As you amble along your new path, ignore the small path that cuts across your path about 30 paces into your journey.  You should be going slightly downhill.  Stop when you get to the fork in the path (and let Kermit and Fozzie drive by…).  One path is smooth going gently downhill, the other goes down at a steeper angle and would require that you watch your step.  Well, take the path at a bearing of F ______ degrees.

When this path finally levels off from going downhill, stop when you meet a “path less traveled” on your left.  Take a bearing of (A+B) ______ degrees.  On that heading, about 2A (double A)______ paces into the woods and up the hill is a (G +1) ______ trunked tree. 

First, make sure no one is around watching you find the box!  (Remember, don’t handle the box if you have food smell on your hands!)  Then go over to the tree and look between the trunks for the first box!!

Move away from the hiding location, taking the box with you (so you don’t draw attention to the hiding place).  Find a comfortable place nearby to “stamp up” (maybe the concrete nearby?).  Clean and dry the stamp before putting it away.

Also in the box you should find a “letterboxers” baggie with maps, the next set of clues, and a small protractor for your use.  (Ignore the “students” baggie unless you want a peek or you are doing their version.) Take one copy of the map and one of the “letterboxer version” slips.  Follow the new directions to determine the location you need to travel to next.

Return the contents of the box (including the protractor for the next letterboxer) to their well-sealed baggies, neatly replace the baggies into the box, and tightly seal the box.  Then, after making sure no one is watching, return the box to its hiding location.  Be sure to cover it with leaves and twigs again so it is not easily seen from any direction and make it look natural!  I thank you, and the next group thanks you!
 

Before you set out read the waiver of responsibility and disclaimer.

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