. Elements of precise surveying and geodesy. Q = BC. sinC, sin(^, + B,\ which may be used in a manner similar to that of the aboveexample. Thus let there be given AB = i meters,BC = meters, B = 135° 50 , and let there beobserved yi, = 75° 56 , ^, z= 68° 34 , andCj = 81° 06 , all of equal weight. Then by a similarprocess it will be found that the adjusted values of theseangles are A^ = 75° 56 , B^ = 68° 34 , andC^ = Si° 06 , and that the two values of BC, computedfrom these, are equal. Prob. 22. Let J^G and GIf he two parts of a straight line, each800
. Elements of precise surveying and geodesy. Q = BC. sinC, sin(^, + B,\ which may be used in a manner similar to that of the aboveexample. Thus let there be given AB = i meters,BC = meters, B = 135° 50 , and let there beobserved yi, = 75° 56 , ^, z= 68° 34 , andCj = 81° 06 , all of equal weight. Then by a similarprocess it will be found that the adjusted values of theseangles are A^ = 75° 56 , B^ = 68° 34 , andC^ = Si° 06 , and that the two values of BC, computedfrom these, are equal. Prob. 22. Let J^G and GIf he two parts of a straight line, each800 feet long. At J^, G, and H are measured the angles whichlines from a station S make with the base, namely, SFG = 40° i2,FGS = 92° 58, and GUS = 43° 55. Compute the length of GSin two ways, and, if they are not equal, find the most probablevalues of the angles which will effect an agreement. 23. The Three-point Problem. In secondary triangulation the position of a station 5 issometimes determined by measuring the angles 5, and S^. subtended at it by three stations A, B, and C whose positionsare known. It is well to measure the three angles at 6 andthen by the station adjustment find the most probable values 23. THE THREE-POINT PROBLEM. 65 of 5, and 5,. The data of the three known points give thedistances AB and BC which will be called a and b, and alsothe angle CBA which will be called B. The problem is todetermine the distances SA, SB, and SC. These distances can be found as soon as the angles A andC are known. Since the sum of the interior angles of thequadrilateral is 360 degrees, A+ C= 360° - B - S,- S,; and since the side BS is common to two triangles, the expres-sions for its length when equated give sin^ b sin5, sinC a sin5,* Thus two equations are established whose solution will giveA and C. Let A -\- C ^ 2m and A — C =^ 2n. The valueof vz is known, namely, m= i8o°-K^ + 5, + 5.), (23) and that of n is to be found. Let V be such an angle that ^ sin5, , ,, t
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