First, solving forwe haveSinceReference to a table of natural functions showsthat the angle with cos equal to 0.87872 measures,to the nearest 1 min., 28°29´.The intervals measured off from A were madeequal for mere convenience. The solution willwork just as well for unequal intervals.In determining the size of an angle by thetangent method, you simply lay off a right triangleand solve for angle A by the common tangentsolution.Suppose that in figure 12-20, you want todetermine the size of angle A. Measure off ACa convenient length (say, 80.0 ft). Lay off CBperpendicular to AC and measure it; say itmeasures 54.5 ft, as shown. The angle is computedby using the following formula:The angle with tangent 0.68125 measures 34°18´.Figure 12-20.-Determining the size of an angle by thetangent method.LAYING OFF AN ANGLE OF A GIVENSIZE.— An angle of a given size can be laid offby tape by applying the tangent right trianglesolution. Suppose that in figure 12-21, you wantto lay off a line AC from A, 25° from line AB,Again measure off a convenient 80.0 ft fromA to establish point B. Erect a perpendicular fromB as shown by the dotted line. You want tomeasure off along this perpendicular side a(opposite side), the distance that, when dividedby the adjacent side, will give the value of thenatural tangent of 25°. Use the following formula:Measure off 37.3 ft from B to establish pointC. A line from A through C will form an angleof 25° from AB.Identifying Chaining Mistakes and ErrorsIn surveying, distinctions are made betweenERRORS and MISTAKES. Errors are caused byfactors such as the effects of nature, the physicalcondition of the personnel performing the survey,and the condition of your instruments. Mistakes,however, are simply human blunders. Whileerrors may be compensated for, mistakes can bedetected, correct, and better yet, prevented onlyby the exercise of care.COMMON MISTAKES.— Mistakes mayresult from poor work habits, lack of judgment,or confusion. They are often costly, time con-suming, and difficult to detect. The easiest wayto avoid them is to establish a definite procedureand follow it, being constantly alert during theFigure 12-21.-Laying off an angle of a given size.12-22
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