Triangles Triangles Everywhere³

-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” (gold) 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 Cosines,  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!³ Letterboxes

Letterboxer Clue Sheet #1

Upper Lake Park (Guenther Picnic Area/Port Washington Veteran’s Park)

Drive to Upper Lake Park in Port Washington, WI.  To get there, first go to the corner of N. Lake St. and E. Jackson St. (This is where the PW marina is, so you can follow the signs.)   Going north on Lake St. from that corner, you should see the PW Veteran’s Park on the right (big band shell with flag) and soon after a place to park on the left.  Park your car in the northernmost parking space in the lot near the sign for the Guenther Picnic Area.  This is where your triangle hunt will begin….

Triangle Spotting (Letterboxers may skip):

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.
 

Data Collection:

Cross the street and go to the Veteran’s Park.  Walk around the park and collect the following information for later use (Note: The letters represent variables that should be assigned the numbers found – the numbers that go on the blanks)

 
Beach hours: A = _____ am to B = _____ pm
No Dogs Allowed Ordinance: C = _____.03 (value of C does NOT include the decimal part)

D = _____ mm Howitzer gun:

Dedicated to Hadler of VFW Post E = ________ and American Legion Post F = _____
Year the bench in honor of the Luxembourg Society of WI was placed: G = 19____
(For ones like these, just the last two digits is the value of the variable.)

Read “The Great Thing” on a rock.  How many lines of text are there to the verse by Holmes? H = _____

When was the Port Washington Yacht Club established (sign above door)? I = 19____

When was the band shell erected? J = 19____

The band shell flag was painted for the K = _____th anniversary of Port Washington.

Once you are done collecting the information, head back to the sand volleyball court in the Guenther Picnic Area.  (You might want to pick up your sand pail on the way….)

Playing in the Sand (Letterboxers may skip, or you can practice your compass skills!):

Place yourself a little southwest of the center of the volleyball court 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!

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

Face yourself at a bearing of 10 degrees.

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

Turn right 144 degrees and sight the new bearing of __________ degrees.

Walk 10 baby steps in that direction.

Turn right another 144 degrees and sight the new bearing of __________ degrees.

Walk another 10 baby steps in that direction.

Turn right another 144 degrees and sight the new bearing of __________ degrees.

(Ah!  You have to make a bearing adjustment!)

Walk another 10 baby steps in that direction.

Turn right another 144 degrees and sight the new bearing of __________ degrees.

Walk another 10 baby steps in that direction.
You should now be back at the beginning, but you’re not done yet!
Now turn left 144 degrees and sight the new bearing of _________ degrees.

Walk another 6.180339887 baby steps in that direction.

(I think you’ll figure out how far this is…)

Turn left another 72 degrees and sight the new bearing of _________ degrees.

Walk another 6.180339887 baby steps in that direction.

Turn left another 72 degrees and sight the new bearing of _________ degrees.

(Ah!  You have to make a bearing adjustment!)

Walk another 6.180339887 baby steps in that direction.

Turn left another 72 degrees and sight the new bearing of _________ degrees.

Walk another 6.180339887 baby steps in that direction.

Turn left another 72 degrees and sight the new bearing of _________ degrees.

Walk another 6.180339887 baby steps in that direction.

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

What shape did you form (be specific) ? ______________________

Note: It doesn’t start with a “P”!

Extra credit: How many triangles are in the design you made? (Don’t count now – do it later!)

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

More Data Collection:

Put your sand pail away (but do take your TTE kit) and then walk north of the volleyball courts.  You should pass a fire hydrant and you should notice a stone wall in the ground.  (On a side note, in the tree line across from the hydrant is a stone pool and waterfall.  I saw five tame deer here while scouting out the area.  They were looking for a handout after drinking from the pool.)

At the north end of this green space, you will come to a spot where you need to make a decision between two paths: the one following the river or the one going uphill.  Take the one that goes at a bearing of (I – H) = _____ degrees, NOT the one that goes at a bearing of (F – D) = ______ degrees!

After a while, you will arrive at the end of this trail.  Passing through the trees and large stones at the end, you will arrive at an open grassy area.  You should see a road ahead of you with a sign along the road to your left.  Go to that sign.

On the road, you should see that there is a pedestrian/bike lane.  The sign you are at tells you how many miles one lap is: L = _____ (include decimal).  Walk south along the road.  What is the speed limit? M = ______  Continue walking south along the road.  You will come to the Lion’s shelter area.  Find the white “Mutt Mitt” box on the pole in the parking lot.  Add the digits of the phone number for the company that makes the “Mutt Mitts” and record it as N = ______ (Include the 800-)  Walk to the shelter.  How many posts are used to hold it up? O = ______  Walk behind the shelter (west).  What picnic area is this? P = ______

Follow the tree line (edge of the trees) south from here.  Shortly you will arrive at a corner that has steps with a green railing leading down.  (Letterboxers can either skip right down to the “Finding Box 1” section and head down the stairs, or if you want to see a great view, continue with the following directions before finding the box.)  Continue along the tree line as it heads east.  You will catch up to the road again and you should head straight south.  Cross the road when it turns downhill, and go up the short drive to an overlook parking lot.  Just to check you’re in the right spot, you should see a green and gold swing set with a blue swing and a red swing.  Walk over to the west end of the parking lot to do the next activities.   This over-look gives you are great view of the marina and downtown Port Washington.  In the next few activities, you’ll need to spot a number of prominent landmarks from here.

Getting Your Bearings Activity (Letterboxers may skip or practice your compass skills!):

Go to the bench on the southwest corner of the over-look.  It has a single medium sized tree next to it.  (Sitting on the bench you would be looking right out at the marina.) 
 

Stand at the edge of the hill by the bench.

Find the bearing to the old lighthouse (look right on top of hill): _____

Find the bearing to the new lighthouse (look left at the end of the breakwater): ______
 

Calculate the angle between these two objects: ______

Finding Box 1 – Triangle Triad:

Walk back to the stairs going down with the green railing.  Once there, you are close to finding the box, so here are a couple of reminders:

 
1) Make sure no one is around watching you find the box!

2) Don’t handle the box or its contents if you have food or lotion smell on your hands!

3) Poke a stick in the box’s hiding spot to scare out any critters before sticking your hand in (just in case)!
 

Go down the stairs.  Note the wood steps.  Stop (or go back up) at the (L x B²) – (A x B) = _____th wood step from the bottom.  To your right (looking down the stairs), approximately “the sum of the digits of M” = _____ paces off the trail, a cave is formed at the roots of a fallen tree.  Look inside this cave for the box.  (It should be well hidden under leaves, bark, and possibly a rock.) Remember how the box is hidden, so you can properly re-hide the box when you’re done (or hide it better).

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 onto your group’s stamp sheet!  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 “letterboxers” baggie.) Take one copy of the map and one of the “student version” clues.  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 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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