## Isosceles #5: Gold Galleons

A cache by KingwoodGeo Message this owner
Hidden : 12/11/2007
In Texas, United States
Difficulty:
Terrain:

Size:  (small)

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### Geocache Description:

This cache is a magnetic key container attached to a metal guard rail. It is NOT at the posted coordinates. This cache is themed "Gold Galleons" because it contains gold-colored coins from around the world. Bring something to write with and be sure to replace the cache on the down-facing part of the railing behind the support post and between the big bolts.

This cache is one of several in a series.

All of the caches are puzzles that involve solving for the location of the apex of an isosceles triange. The base of the isosceles triangle is the line that connects two water towers in Kingwood. The cache is located at the apex that satisfies a condition that is specified below.

Tower #1 is located on Kingwood Drive near East End Park.
Its coordinates are: 30° 3.5293 -95° 9.3855
UTM coordinates: X= 292115 Y=3327263

Tower #2 is located on Woodland Hills Drive near the High School Agricultural Sciences Barn.
Its coordinates are: 30° 1.9972 -95° 13.0668
UTM coordinates: X= 286144 Y=3324545

The cache is located at the apex of an isosceles triangle located 3315 meters from the center of the baseline and equidistant from both water towers. The cache is SOUTH of the baseline.

The cache is magnetically attached to a traffic guard rail at one of its support post. It's between some big bolts.

[An isosceles triangle has two sides that are the same length. The third side is called the base.
The apex of an isosceles triangle is always exactly the same distance from the other two corners.
A line constructed at 90 degrees to the baseline through the midpoint of the base will pass through all possible solutions for isosceles triangles with that specific base.
The midpoint of any line is simply the average of the endpoint coordinates.
The Pythagorean Theorem relates the side lengths of right triangles. An isosceles triangle can be thought of as a right triangle joined with its mirror image along the midpoint bisector line.
All calculations should be done in Universal Transverse Mercator meters. Use (visit link) to transform coordinates between LatLon and UTM meters. (If that does not work, try using your GPS as a calculator by switching your GPS between decimal minutes and UTM. Create a waypoint in one system, then change the system and view the waypoint details in the other system. Very clunky, but it does the job.)
Ignore the Earth's curvature for distances this close.
The slope of a line is M=(Y1-Y2)/(X1-X2)
The equation of a line is Y=Slope * X + Intercept
To solve for an intercept, rewrite the line equation with only Y on one side of the equals sign and substitute the value of the slope and the X and Y of a point known to lie on the line.
Given a line of slope M, the slope of any line perpendicular to that line is -1/M]

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)

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