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TYPES OF TRIANGULATION NETWORKS - 14071_361
TRIANGULATION  STATIONS,  SIGNALS, AND INSTRUMENT SUPPORTS

Engineering Aid 2 - Intermediate Structural engineering guide book
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Figure 15-17.—Chain of quadrilaterals. triangles  ADB, ADC, CDE,  and EDF, in that order, or by solving triangles  ADB, BDF,  and FDE, in that order. You can also see that this system can be used to cover a wide territory. It can cover an area extending up to approximately  25,000  yards  in  length  or  breadth. Chain of Quadrilaterals A quadrilateral, too, is technically a polygon; and a chain of quadrilaterals would be technically a chain of polygons.  However,  with  reference  to  triangulation figures, the term  chain of quadrilaterals  refers to a figure arrangement like that shown in figure 15-17. Within each of the quadrilaterals shown, the triangles on which computations are based are not the four adjacent triangles  visible  to  the  eye,  but  four  overlapping triangles—each  of  which  has  as  sides  two  sides  of  the quadrilateral and one diagonal of the quadrilateral. For example,  in  quadrilateral  ACDB  there   are   four overlapping triangles as follows:  ADC, ADB, ABC, and BCD. You can see that solving these four triangles will give  you  two  computations  for  the  length  of  each unknown  side  of  the  quadrilateral. Consider, for example, the quadrilateral  ACDB. Look at angle BAC. We will call the whole angle at a comer by the letter (as, angle A) and a less-than-whole angle at a corner by the number shown (as, angle 1). The angles at each station on the quadrilateral, as measured with a protractor to the nearest 0.5 degree and estimated to the nearest 0.1 degree, are sized as follows: The  angles  that  make  up  each  of  the  four overlapping  triangles,  together  with  their  natural  sines, are as follows: Note that the total sum of the angles is 360°, which it should be for a quadrilateral, and that the sum of the angles  in  each  triangle  is  180°,  which  is  also geometrically  correct. To solve the quadrilateral, you solve each of the overlapping triangles. First, you solve triangle ABC for sides AC and BC, using the law of sines as follows: Then,  using  similar  computation  procedures,  you solve triangle  ABD for sides BD and AD, triangle ADC 15-26







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