Each degree of latitude stretches for approximately 69 miles (or 111km) while the distance between degrees of longitude is measured as: cosine (longitude) * 69.172 miles.
So I think it's cool to live so close to a "degree confluence" (where a latitude/longitude line meet) like this one.
To find this cache, you will need to use some math called "Great Circle Distance" which deals with the shortest distance between two points over a curved surface like the Earth.
Using this math, you can either determine the range and bearing between two points or find a second set of coordinates based on an initial coordinate and range and bearing from there.
To find this cache, you will use a given range and bearing from the confluence to find the cache.
Given:
Distance (dist) = 0.2222 miles (1,173.22 feet)
Bearing (brng) = 037.055 Degrees
Initial latitude (lat1) = 43
Initial longitude (lon1) = -88
1) To start, convert the initial latitude , longitude and bearing to radians.
lat1R = lat1 * Pi/180
lon1R = lon1 * Pi/180
brngR = brng * Pi/180
2) Next, we need to convert the distance to a fraction of the radius of the Earth (3959.8728 miles)
distR = dist / 3959.8728
3) Now the hard stuff. We have a bunch of trigonometry to do. Don't worry… these equations plug into a spreadsheet nicely.
lat2R = asin( sin(lat1R) * cos(distR) + cos(lat1R) * sin(distR) * cos(brngR) )
lon2R = lon1R + atan2( cos(distR) - sin(lat1R) * sin(lat2R), sin(brngR) * sin(distR) * cos(lat1R) )
4) Now we convert the coordinates back from radians to degrees
lat2 = lat2R * 180/Pi
lon2 = lon2R * 180/Pi
These coordinates will be in decimal degree format (DD.ddddd) while geocaching.com uses degree decimal minute format (DD MM.mmm) but there are plenty of conversion tools around for that part.
You can check your answers for this puzzle on GeoChecker.com.
Please make sure to put the container back precisely so it is secure and out of site. Thanks!
Happy hunting!
Special thanks to Pawn-of-Chaos for the support in rebooting his cache as well as his help in pre-emptively troubleshooting/proof-reading the cache and to everyone who has provided additional suggestions and corrections.