Triangles and Tribulations Multi-Cache

TRIANGLES and Tribulations

This cache will test your patience and (hopefully) challenge you! We are a big fan of caches where the cacher has to solve a puzzle to find the final location. This cache has a lot of the things we like about caching.

This is a multi cache with several locations with driving or possibly biking between each location. You will need to use your noggin and do some research (All the means to solve this cache are on math web sites, math textbooks and math books in the library.) before you attempt this cache

I'm not going to give you any help in figuring out the formulas needed to solve each step, but I will give you all the information you’ll need to solve each problem. You’ll need to ask your 17 year old child, niece or nephew, or try to find a math whiz if you aren’t one already.

Here's what I suggest:

• Calculator (preferably a scientific one), pen/pencil and paper.
• Read the cache steps VERY carefully, and make sure you have all that you’ll need.
• The ability (or desire) to do some simple? geometry & trigonometry (I see some of you cowering already!) Don't be a chicken!!! (bawk bawk!)
• Biking (weather permitting) this cache, especially if you are not familiar with the quirks of Downtown Madison. I've lived here nearly 10 years, and it still "drives" me nuts. It is about 10-12 miles round trip. Madison is well known for its bike commuter paths.

You’ll need to complete all the steps to find the final cache. Each step will give you a number which will be used in the calculations of the final coordinates. Be sure to round to the nearest whole number for ALL calculations. Pay close attention to the "given" values and to detail. Also, be sure to use the measurements I've given. The EXACT measurements for the physical objects used do vary from reality. You won't actually have to measure any thing for this cache as I knew that would cause too many variables. If you follow the directions I give, you will find the cache. :)

Step 1. Find out the volume (in cu. ft.) the specially shaped building 

The waypoint coordinates are for parking. Please don't park in the permit lot, park in the strip mall parking lot. After you park, walk to and stand on the storm drain at N43° 04.569 W89° 27.302 The 13-story building in front of you is probably one you know of and drive past periodically. It is named Pyare Square. That name will/may be funny soon.

Imagine a line from the storm sewer to the top of the building. 

You'll need to find a micro  (N43° 04.622 W89° 27.201) that has the angle from the building to that line, and the distance from the sewer drain to the top of the building. Assume that the angle from the building to the ground is 90º.

Once you find the micro, you will have enough information to complete Step 1. It has the info you need but please leave the information there and don't take it with you. Copy the information down.

You also may want to draw a picture to help you.

What is the volume of the building (assuming it is a perfect geometric shape)?

__________Cu. ft.

After you have the answer, Go to N43° 04.482 W89° 22.918 There is a lot of parking in the area which should be obvious. Step 2 and 3 are all within walking distance.

Step 2. 

What is the circumference of the flowerbed?  (Be sure to visit this in April-May, The tulips here are gorgeous!)

The information you’ll need  to complete this step is “hidden” nearby.  Standing on the square base a few feet north of the flowerbed, walk approximately 90 feet at a compass bearing of 7º true.

Hint: gur bayl gjb qvtvg ahzore gung vf ba gur fvta gjvpr.

Hidden number_______ft.                 Circumference  _________ft. 

Step 3.

How long is the hypotenuse side of the triangle shaped city block?

The block you are standing on is a triangle. (who would have thought?) It goes from

Vertex T1 (N43º 04.486 W89º 22.893) to 

Vertex T2 (N43º 04.484 W89º 22.827) to 

Vertex T3 (N43º 04.505 W89º 22.860.)

I’m going to give you 2 of the 3 lengths of the sides. Side 1 (T1 to T3) and Side 2 (T2 to T3) (Better draw another picture!)

You’ll need to find the length of the hypotenuse Side (T1 to T2)

Find the micro that will give you the 2 lengths at N43º 04.488 W89º 22.830

Be very discreet here. There are lots of eyes upon you. This is NOT on private property, so no need to search the parking lot or fence.

How long is the side of the triangle shaped city block? ______ft.

By the way...Why are there so many of these triangle shaped blocks? If you look at a Madison map you notice that downtown Madison is on an Isthmus, which runs NE to SE. But the 4 capitol sides face North East West South, so the streets that serve the capitol AND the orientation of the Isthmus criss-cross forming triangles, which make downtown navigation quite interesting!

The final location is at N43° 03.AAA  W89° BB.CCC

1. Take the cylinder's volume, get the square root, then add 246. This will be AAA.
2. Take the flowerbed's circumference and subtract 51. This will be BB.
3. Take the City block's length and add 137.  This will be CCC.

Again, make sure you have carefully done your math and rounded to the nearest whole number. Accurate math counts on this cache. Good Luck!

The final location is a few miles from here, so hop back in your car or bike and head over. 

PLEASE PLEASE PLEASE--- Re-hide the cache with care and better than you found it! (This is a 5, remember?) There are no hints to the final cache, but if you have trouble with the math, send me what you have and I'll point you in the right direction.

We hope you enjoyed going through Triangles and Tribulations as much as we enjoyed setting it up!