MATH041 - Trigonometry - Triangulation

Triangulation is the process used to determine the location of a distant point by measuring the observed angles of the line-of-sight to that point from two different locations. In other words, given one side of a triangle, and two angles, one can determine the lengths of the other sides. Triangulation has many applications from radar to motion capture, but was initially used for surveying.

By covering the topic of triangulation, this course will introduce many of the concepts of trigonometry, the study of triangles and trigonometric functions.

• Introduction
• Review of the Geometry of Triangles
  • Angles and their Measure
  • The Triangle
    • Definition, Notation, and Properties
    • The Right Triangle
      • The Pythagorean Theorem
      • Definition of the Trigonometric Functions
      • A Trigonometric Identity
    • Classification of Triangles
• The Law of Sines
• Basic Triangulation
• Introduction to Vectors
  • Representation
  • Unit Vectors
  • Multiplication by a Scalar
  • Addition and Subtraction
  • The Angle Between Two Vectors
  • The Dot Product
• Coordinate Systems
  • Cartesian Coordinates
  • Spherical Coordinates
  • Azimuth, Elevation, and Range Coordinates
• The Theodelite
• Advanced Triangulation
• Applications
  • Traditional Surveying and Mapmaking
  • Definition of the Meter
  • Distance to the sun, moon, and stars
  • Other Applications
• Summary

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