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How to Calculate the Position & UTM With the Pythagorean Theorem

The Universal Transverse Mercator (UTM) uses the system of latitude and longitude from the 80 degree south to 84 degree north latitudes. UTM lines are measured in meters and are presented in a grid format used to work in compendium with the Northing and Easting coordinates of a map. Triangulation of a location on a map can be achieved by using a UTM map and the Pythagorean Theorem, A^2+B^2=C^2, which identifies an unknown length of the side of a triangle as long as two other sides are known.

Things You'll Need

UTM map
UTM grid
Scientific calculator
Pencil
GPA device

Instructions

- 1
  Locate an area on the UTM map as a reference point. Choose an area with an easily identifiable topographical landmark such as a mountain or ravine.
- 2
  Identify a second area on the UTM map that features an easy to identify topographical feature such as a stream. Choose this area based on a slant from the first area. This slant will later become the hypotenuse of the right triangle.
- 3
  Draw a straight line connecting the two reference points.
- 4
  Draw a line protruding from each reference point until the two lines overlap, forming a right triangle, to triangulate a position.
- 5
  Overlay the UTM grid to the UTM map. Each square on the UTM grid represents 100 meters.
- 6
  Count the number of grid spaces for both the length and height of the triangle. The length of the triangle will be referenced as "A," the height will be referenced as "B," and the slope as "C."
- 7
  Solve the Pythagorean Theorem for "C" by squaring the values of "A" and "B" and adding them together. Take the square root of the sum of this equation to determine the distance of "C," the slope of the triangle.

Nature