from one line to another is to use a surveyinginstrument called a transit. However, if you do nothave a transit, you can locate the corner points withtape measurements by applying the Pythagoreantheorem. First, stretch a cord from monument A tomonument B, and locate points C and D by tapemeasurements from A. Now, if you examinefigure 5-16, you will observe that straight linesconnecting points C, D, and E form a right trianglewith one side 40 feet long and the adjacent side 35feet long. By the Pythagorean theorem, the length ofthe hypotenuse of this triangle (the line ED) is equalthe square root of 35^{2 }+40^{2}, which is approximately53.1 feet. Because figure EG DC is a rectangle, thediagonals both ways (ED and CG) are equal.Therefore, the line from C to G should also measure53.1 feet. If you have one person hold the 53. 1-footmark of a tape on D, have another hold the 35-footmark of another tape on C, and have a third personwalk away with the joined 0-foot ends, when the tapescome taut, the joined 0-foot ends will lie on thecorrect location for point E. The same procedure, butthis time with the 53. 1-foot length of tape runningfrom C and the 35-foot length ruining from D, willlocate corner point G. Corner points F and H can belocated by the same process, or by extending CE andDG 20 feet.PERPENDICULAR BY 3:4:5 TRIANGLEIf you would rather avoid the square rootcalculations required in the Pythagorean theoremmethod, you can apply the basic fact that any trianglewith sides in the proportions of 3:4:5 is a righttriangle. In locating point E, you know that this pointlies 35 feet from C on a line perpendicular to the baseline. You also know that a triangle with sides 30 and40 feet long and a hypotenuse 50 feet long is a righttriangle.To get the 40-foot side, you measure off 40 feetfrom C along the base line; in figure 5-16, thesegment from C to D happens to measure 40 feet.Now, if you run a 50-foot tape from D and a 30-foottape from C, the joined ends will lie on a lineperpendicular from the base line, 30 feet from C.Drive a hub at this point, and extend the line to E (5more feet) by stretching a cord from C across themark on the hub.BATTER BOARDSHubs driven at the exact locations of buildingcorners will be disturbed as soon as the excavation forthe foundation begins.To preserve the cornerlocations, and also to provide a reference formeasurement down to the prescribed elevations,batter boards are erected as shown in figure 5-17.Each pair of boards is nailed to three 2-by-4corner stakes as shown. The stakes are driven farenough outside the building lines so that they will notbe disturbed during excavation. The top edges of theboards are located at a specific elevation, usuallysome convenient number of whole feet above asignificant prescribed elevation, such as that at the topof the foundation. Cords located directly over thelines through corner hubs, placed by holding plumbbobs on the hubs, are nailed to the batter boards.Figure 5-17 shows how a corner point can be locatedin the excavation by dropping a plumb bob from thepoint of intersection between two cords.Figure 5-17.—Batter boards.5-12