Triangles Triangles Everywhere2

-Letterboxer's Version-

 

Originally Placed: March 31, 2006

By: “The Dragon”

Location: Washington and Waukesha Counties, WI

Difficulty: Depends on your math ability, but not too tough (see links below).

Terrain: Easy (Mostly flat with some moderate climbing, some places can get pretty "mushy" after lots of rain or thawing snow.)

Number of Boxes: 3

Time: 1-3 hours.

Dragon's Home Page

 
CAMOUFLAGED BOX
 

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, Law of Cosinesreference 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!2 Letterboxes

Letterboxer Clue Sheet #1

 

Sussex Village Park

Drive to Sussex Village Park located on Cty W (Silver Spring Rd) at Weaver Dr. in Sussex.  (It is across from Faith Lutheran Church).  Drive south on Weaver Dr. into the park and turn left when the tennis courts are to your right into the wide drive before the large shelter.  Drive back as far as you can into the higher parking lot by the brown building (which is the disc golf headquarters for the park).  Park in this lot for this is where you’ll begin your journey.

Triangle Spotting:

During your letterboxing adventure you should spot many uses of triangles.  Use the spaces below to describe at least 10 ways you see triangles being used other than the ways pointed out on the clue sheets.  Keep this activity in mind, and don’t forget to complete it as you go.
 

1)________________________________

2)________________________________

3)________________________________

4)________________________________

5)________________________________

6)________________________________

7)________________________________

8)________________________________

9)________________________________

10)_______________________________


Take a look around the park while remaining in the parking lot, and note where the tennis courts and the volleyball courts are.  Then walk east further up the hill on the other side of the brown disc golf building.  Spot the older playground and go to it.

Ok, so THIS playground doesn’t have a merry-go-round, and none of the other parks do either.  They are going extinct! L  Please do what you can to save the merry-go-rounds in your community!
 

Getting Your Bearings Activity (letterboxers, you might try this activity, or skip it):
 

Stand on the north side of the red swing set, but not too close so the metal doesn’t interfere with the magnetic compass.

From where you are standing, find the bearing to the cross atop Faith Lutheran: ______

 

Find the bearing to the large oak tree that is a ways behind the yellow fire hydrant: ______

 

Calculate the angle between these two objects: ______

 

Data Collection:

Before leaving the playground, find and record the following information:

Read the park rules.
Record the opening hour of the park as A= ______
Record the Village Code Chapter that covers these rules as B = _____
Record the number of seats on the teeter-totter (spring see-saw) as C = _____
(Note: Yet another fun device has succumbed to lawyers.  There were 4 seats.)
Record the number of slides in this playground as D = _____
Record the number of blue swings in this playground as E = _____

Now go to the yellow post just to the east of this playground.
It indicates the tee (or “launch pad”) for a disc golf hole. 
Record the hole number as F = ______. 
Record the length of the hole as G = _____ feet. 
Record the area code of the sign maker’s phone number as H = _____,
then the next three digits of the number as I = _____,
and the last four digits of the phone number as J = ______.

 

Now walk north from this tee on the path.  Soon you’ll come to a wire with a yellow plastic sheath on it.  This wire forms a triangle with the ground.  How does this triangle serve a purpose with this contraption?



FIRE! FIRE!  Quick!  Run to the yellow fire hydrant you saw from the red swings!  Record the year on the fire hydrant as K = _______.  Find the number above the “K10B” and record it as L = _____.

Fire’s out!  Continue north from the hydrant.  Hmm, more park rules.  Hmm, maybe the hydrants are yellow from all the dogs in the park. :-P   Ah, but you do have to clean up their poo.  Record the amount of the fine for not cleaning up your dog’s poo as M = _______.

Continue on north to that big oak tree.  This is a very special tree!  Read the sign about it and record the following information:
Year the tree was discovered in: N = _______
Year a plaque was first placed: O = ______
Year the tree became the village’s logo: P = ______
The tree was determined to be Q = ______ years old in 1982.
The tree was R = ______ years old when the Declaration of Independence was signed.
The tree was S = ______ years old when the first pioneer came.
The tree was T = ______ years old when Sussex became a village.
The tree was U = ______ years old when Sussex bought the land to be a park.
The year this sign was placed: V = _______

Travel a little further north on the path to another disc golf tee.
This is hole number W = ______ and its distance is X = _______ feet.

Enough data collection for now!  Remember where the volleyball courts are?  Take a hike over to them.  Along the way, you might pick up your sand pail….
 

Playing in the Sand (letterboxers, you might try this student activity or skip it):

(Note: If both of these VB courts are being used, you can either use the sandy baseball infield nearby, or do this activity on another sand VB court at each of the next parks you’ll go to.)

 

Place yourself in the middle of one of the courts so you have lots of room to move.
Also, remember that bearings only go from 0 to 360, so if you go over 360 or under 0, you’ll need to subtract 360 or add 360 to find the true bearing!

Face yourself at a bearing of 315 degrees.  Take 5 baby steps (heel to toe) in that direction.

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

Turn 90 degrees to the right and sight the new bearing of __________ degrees.

Walk 5 baby steps in that direction.

Turn 45 degrees to the left and sight the new bearing of __________ degrees.

Walk  baby steps in that direction.

Turn 45 degrees to the left and sight the new bearing of __________ degrees.

Walk another 5 baby steps in that direction.

Turn 90 degrees to the left and sight the new bearing of __________ degrees.

Walk another 5 baby steps in that direction.

Turn 135 degrees to the left and sight the new bearing of __________ degrees.

Walk another  baby steps in that direction.

Turn 135 degrees to the right and sight the new bearing of __________ degrees.

Walk another 5 baby steps in that direction.

Turn 90 degrees to the left and sight the new bearing of __________ degrees.

Walk another 5 baby steps in that direction.

Turn 135 degrees to the right and sight the new bearing of _________ degrees.

Walk another  baby steps in that direction.

Turn 45 degrees to the left and sight the new bearing of __________ degrees.

Walk another 5 baby steps in that direction.

Turn 90 degrees to the left and sight the new bearing of __________ degrees.

Walk another 5 baby steps in that direction.

Turn 135 degrees to the left and sight the new bearing of __________ degrees.

Walk another  baby steps in that direction.

Turn 135 degrees to the right and sight the new bearing of ___________ degrees.

Walk another 5 baby steps in that direction.

Turn 90 degrees to the right and sight the new bearing of __________ degrees.

Walk 5 baby steps in that direction.

Turn 135 degrees to the left and sight the new bearing of ___________ degrees.

Walk another  baby steps in that direction.

You should now be back at the beginning, but….
Turn 90 degrees to the right and sight the new bearing of __________ degrees.

Walk baby steps in that direction.

Turn 135 degrees to the left and sight the new bearing of __________ degrees.

Walk another 5 baby steps in that direction.

Turn 90 degrees to the right and sight the new bearing of __________ degrees.

Walk 5 baby steps in that direction.

Turn 135 degrees to the left and sight the new bearing of __________ degrees.

Walk another  baby steps in that direction.

Turn 135 degrees to the right and sight the new bearing of __________ degrees.

Walk another 5 baby steps in that direction.

Turn 90 degrees to the right and sight the new bearing of __________ degrees.

Walk 5 baby steps in that direction.

Turn 45 degrees to the right and sight the new bearing of __________ degrees.

Walk baby steps in that direction.

Turn 45 degrees to the right and sight the new bearing of __________ degrees.

Walk 5 baby steps in that direction.

Turn 90 degrees to the right and sight the new bearing of __________ degrees.

Walk 5 baby steps in that direction.

You should now be back at the beginning, and you’re done!


What shape did you form (be specific) ? ______________________

If you don’t know now (probably not), you’ll know when you find the second box!
Build a sand castle in the middle! Don’t forget to take a picture! J
After you are done playing in the sand, be sure to smooth out the sand so you don’t leave any trace of your work for others to see.  (Have fun destroying your creation!)

Finding Box 1 – Triangle Starburst:

Before leaving the VB area, make a note of the numbers on the homerun fence nearby and record it as Y = ______.  Then head northwest to the snack shack.  There, find the address and record the four digit number after the “N” as Z = ________.

Now walk to the tennis courts.  Before you get there, you will come to a path that leads west then south into some woods.  The woods are flanked on one side by a row of evergreens and on the other by a pile of rocks.  The woods in between have a number of pines planted in nice even rows.  Believe it or not, there are a few disc golf holes that go through the woods here, so look out for flying saucers and don’t interfere with anyone’s play – just wait until they get out of your way, which shouldn’t take long.
Don’t forget to make sure no one is around watching you find the box!  (Remember you also shouldn’t handle the box if you have smelly hands!)

To find the first box, you need to find disc golf tee (launch pad) number (Y/M) x (D x L) = ______.  Once there, take a bearing of (H – F) = ______degrees and walk (the first two digits – the last two digits of Z) = _____ paces to a large tree growing in the rocks.  Take (U – X) = ______ paces to the right, and look under the rock that looks like Tennessee for the first box!  (It may be under a few more rocks.) Remember how the box is hidden, so you can properly re-hide the box when you’re done.

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”. Don’t forget this includes putting your stamp image(s), names, date, and a nice note into the letterbox logbook and to stamp the box’s stamp into your logbook!  Use the rags to clean and dry the stamp before putting it away.

Also in the box you should find a “students” baggie with maps and the next set of clues.  (Ignore the “students” baggie.) Take one copy of the map and one of the blue “letterboxers version” slips.  Follow the new directions to determine the location you need to travel to next.

Return the contents of the box 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 the rocks again so it is not easily seen from any direction and make it look natural!  Make sure Tennessee is on top too!  I thank you, and the next group thanks you!

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

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