Figure 15-17.—Chain of quadrilaterals.triangles ADB, ADC, CDE, and EDF, in that order, orby solving triangles ADB, BDF, and FDE, in that order.You can also see that this system can be used to cover awide territory. It can cover an area extending up toapproximately 25,000 yards in length or breadth.Chain of QuadrilateralsA quadrilateral, too, is technically a polygon; and achain of quadrilaterals would be technically a chain ofpolygons. However, with reference to triangulationfigures, the term chain of quadrilateralsrefers to afigure arrangement like that shown in figure 15-17.Within each of the quadrilaterals shown, the triangles onwhich computations are based are not the four adjacenttriangles visible to the eye, but four overlappingtriangles—each of which has as sides two sides of thequadrilateral and one diagonal of the quadrilateral. Forexample, in quadrilateral ACDB there are fouroverlapping triangles as follows: ADC, ADB, ABC, andBCD. You can see that solving these four triangles willgive you two computations for the length of eachunknown side of the quadrilateral.Consider, for example, the quadrilateral ACDB.Look at angle BAC. We will call the whole angle at acomer by the letter (as, angle A) and a less-than-wholeangle at a corner by the number shown (as, angle 1). Theangles at each station on the quadrilateral, as measuredwith a protractor to the nearest 0.5 degree and estimatedto the nearest 0.1 degree, are sized as follows:The angles that make up each of the fouroverlapping triangles, together with their natural sines,are as follows:Note that the total sum of the angles is 360°, whichit should be for a quadrilateral, and that the sum of theangles in each triangle is 180°, which is alsogeometrically correct.To solve the quadrilateral, you solve each of theoverlapping triangles. First, you solve triangle ABC forsides AC and BC, using the law of sines as follows:Then, using similar computation procedures, yousolve triangle ABD for sides BD and AD, triangle ADC15-26

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