Applications of Trigonometry
      Applications of Trigonometry in Geodesy (or Plane Surveying)
      Applications in geodesy or plane surveying
Applications of Trigonometry in Geodesy (or Plane Surveying)
Applications in geodesy or plane surveying

In plane surveying of geographical features, boundaries and areas are determined by the measurement of points and lines of direction on the earth's surface. Obtained horizontal and vertical distances and angles are then processed using computations based on geometry and trigonometry.

For example, to determine distance x between points, C and D, which cannot be measured directly, measured is the distance d between accessible points A and B and angles a1, a2 and b1, b2.   
In  DABC,
and in DABD,
 
applying the cosine law in the triangle ACD,
 
Example:   A ground in form of a quadrilateral should be divided into two equal areas, see the below figure.
At what distance from the vertex C dividing line segment AE intersects the side BC if lengths of sides are, b = 24 m, c = 28 m and d = 45 m, and angles b = 57 and d = 115.
Solution:  In DACDe2 = b2 + c2 - 2bc cosd,   e = 43.9 m,
since b + e  + j = 180,   j = 180 - (e  + b) = 6344′19″.
The area of the quadrilateral ABCD as the sum of triangles ACD and ABC,
The area of the triangle ABE is required to be half of the area of the quadrilateral, thus
Geometry and use of trigonometry contents - B
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