How to Use Algebra As a Land Surveyor

Although land surveying has a strong quantitative aspect, the job is an art as much as a science. Thomas M. Cooley, a chief justice of the Michigan Supreme Court, wrote in the late 19th century that the surveying profession was prone to subjective error. That is still true today, and it can lead to legal complications. Precise measurements and calculations help to minimize this possibility. Algebra and trigonometry -- a subset of algebra applied to geometry -- are useful in predicting distances, heights and angles of various natural features. Data on erosion and water level changes help land surveyors predict prospects for construction projects in the near future.

Things You'll Need

  • Land surveying equipment
  • Calculator
  • Global Positioning System data
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Instructions

    • 1

      Simplify calculations by taking advantage of trigonometric functions. Often, triangle-based geometry will use some combination of sine (sin), cosine (cos) and tangent (tan) operations to deduce unknown variables. For instance, a surveyor 300 meters away from a vertical feature needs to position a sighting instrument 10 degrees above the horizontal plane to pinpoint the top of the feature.

      Here, the tangent (tan) function comes in handy. Assume that the feature is at right angles to the horizontal. By definition, tangent(angle) = vertical/horizontal. In this case,

      tangent(10 degrees) = vertical/300. Therefore, 300*tan(10 degrees) = vertical, or 52.898 meters above the level of the measuring instrument.

    • 2

      Combine natural and human factors to make predictions about the environment. Make recommendations accordingly. For instance, say a lake's water level rises or falls according to an equation that relates average annual temperature and water level. Land surveyors would use that equation to predict the water level in the near future.

    • 3

      Limit algebraic extrapolations. Equations and formulas usually do not capture the "feedback" and cyclical nature of natural phenomena -- or, if they do, they become exceedingly complicated. This is especially true with water-related surveying, as water levels are more responsive to temperature, pollution and other external conditions. Acid rain may alter lake chemistry. The modified lake water may erode subsurface features, carving out bigger niches for water to flow into, thereby reducing the rate of water level rise. Limitations on data, equipment, time, and expertise all serve to introduce unavoidable error into predictions about the future, no matter how skilled the surveyor.

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