from one line to another is to use a surveying
instrument called a transit. However, if you do not
have a transit, you can locate the corner points with
tape measurements by applying the Pythagorean
theorem. First, stretch a cord from monument A to
monument B, and locate points C and D by tape
measurements from A. Now, if you examine
figure 5-16, you will observe that straight lines
connecting points C, D, and E form a right triangle
with one side 40 feet long and the adjacent side 35
feet long. By the Pythagorean theorem, the length of
the hypotenuse of this triangle (the line ED) is equal
the square root of 352 +402, which is approximately
53.1 feet. Because figure EG DC is a rectangle, the
diagonals both ways (ED and CG) are equal.
Therefore, the line from C to G should also measure
53.1 feet. If you have one person hold the 53. 1-foot
mark of a tape on D, have another hold the 35-foot
mark of another tape on C, and have a third person
walk away with the joined 0-foot ends, when the tapes
come taut, the joined 0-foot ends will lie on the
correct location for point E. The same procedure, but
this time with the 53. 1-foot length of tape running
from C and the 35-foot length ruining from D, will
locate corner point G. Corner points F and H can be
located by the same process, or by extending CE and
DG 20 feet.
PERPENDICULAR BY 3:4:5 TRIANGLE
If you would rather avoid the square root
calculations required in the Pythagorean theorem
method, you can apply the basic fact that any triangle
with sides in the proportions of 3:4:5 is a right
triangle. In locating point E, you know that this point
lies 35 feet from C on a line perpendicular to the base
line. You also know that a triangle with sides 30 and
40 feet long and a hypotenuse 50 feet long is a right
To get the 40-foot side, you measure off 40 feet
from C along the base line; in figure 5-16, the
segment from C to D happens to measure 40 feet.
Now, if you run a 50-foot tape from D and a 30-foot
tape from C, the joined ends will lie on a line
perpendicular from the base line, 30 feet from C.
Drive a hub at this point, and extend the line to E (5
more feet) by stretching a cord from C across the
mark on the hub.
Hubs driven at the exact locations of building
corners will be disturbed as soon as the excavation for
the foundation begins.
To preserve the corner
locations, and also to provide a reference for
measurement 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-4
corner stakes as shown. The stakes are driven far
enough outside the building lines so that they will not
be disturbed during excavation. The top edges of the
boards are located at a specific elevation, usually
some convenient number of whole feet above a
significant prescribed elevation, such as that at the top
of the foundation. Cords located directly over the
lines through corner hubs, placed by holding plumb
bobs on the hubs, are nailed to the batter boards.
Figure 5-17 shows how a corner point can be located
in the excavation by dropping a plumb bob from the
point of intersection between two cords.
Figure 5-17.Batter boards.