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How to Calculate the Height of a Tree With a Tangent Angle

The height of a tree can be closely estimated with the aid of math and a clinometer. Data on tree height can be used by forest ecologists as one measure of general forest health. Using principles of trigonometry to determine tree height can save significant time and money compared to other means of surveying. Clinometers are forestry devices which can be used to obtain the angle between eye level and the top of the tree.

Things You'll Need

  • Measuring tape
  • Clinometer
  • Notepad
  • Calculator
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Instructions

    • 1

      Choose a place to stand at least several feet from the base of the tree. Enlist the help of a second person and a measuring tape to determine the precise distance in feet. Record this measurement.

    • 2

      Place the clinometer at eye height. Use the device to record the angle between yourself and the top of the tree. Record this angle, the theta value.

    • 3

      Use the values obtained to begin height calculations. Use the calculator to obtain the tangent value of the estimated angle. The tangent of a 17-degree angle is 0.31.

    • 4

      Multiply the tangent value by the distance between yourself and the tree base. If the distance was 50 feet and the tangent value 0.31, the result would be 15.3 feet.

    • 5

      Mathematically adjust for holding the clinometer at eye height. Use the measuring tape to determine the distance between the eyes and the ground. Add this to the previously determined measurement. If your eyes are 5 1/2 feet off the ground and initial calculations yielded the value of 15.3, the adjusted height of the tree is 20.8 feet.

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