Title of Activities: TRILATERATION METHODS
Objective:
a. To gather data for a low order trilateration system consisting of a chain of single
triangles
b. To learn how to apply the approximate method of adjusting a trilateration system
and how to determine angle of its unknown sides
Instruments:
Theodolite or Engineer’s transit, steel tape, range poles, chaining pins, and hubs or pegs
Procedure:
1. Establish the station at designated places on the area assigned to be surveyed. Call these
stations A, B, C, and so forth (See accompanying sample sketch). Use pegs or hubs to
mark these stations.
2. Designate point A and point E as the base line and check base respectively. Measure
precisely each exterior angle in two trials and record the mean measurement as the
actual exterior angle of each point.
3. Set up and orient the theodolite (or transit) at A then, determine the bearing (or
azimuth) of AB.
4. At station A, measure the relevant length for the line connected to this point and record
the observed values accordingly.
5. Repeat the preceding procedures of setting up the instrument and measuring horizontal
angles at all other designated trilateration stations.
6. Tabulate observed and calculated values accordingly. Refer to the accompanying sample
formats for the tabulation of field data. Note: determine the average length of the same
line taken from the different point (sample AB and BA).
MEASURED MEAN
STATION LINE
LENGTH LENGTH
AB
AC
A
AD
BA
B BC
CA
CB
C CD
CE
DA
DC
D
DE
EC
E ED
VALUE FROM STATION COMPUTED
TRIANGLE LINE
ADJUSTMENT ANGLE
AB
BC
ABC
CA
CD
DA
ACD
AC
DE
EC
CDE
CE
Computation:
1. The average value of each measured angle is determined by dividing the total angle
accumulated on the circle by the number of repetitions. The total angle may be larger
than 360 degree, making it necessary to add a multiple of 360 degree to the reading
prior to dividing.
2. Station Adjustment:
a. Adjust the common length of each triangle by taking the mean of the measured
length. This will be used for determining the interior for every triangle.
3. Figure Adjustment:
a. A final adjustment is made to see to it that the sum of the adjusted interior angles of
any single triangle in the system is equal to 180 degrees after station adjustment.
b. If the above condition is not satisfied, the correction is determined by subtracting
the sum of the interior angles of any single triangle from 180 degree and dividing by
the number of interior angles. This computed may be a positive or a negative
quantity.
c. The adjusted values of interior angles of the triangle are then determined by adding
algebraically to each measured and averaged value the computed correction for the
particular triangle.
d. As a check the sum of the adjusted interior angles of any single triangle should now
equal to 180 degrees.
4. Computing Interior for Every Triangle:
a. Starting with the first triangle (ABC), the interior angle of point A may be computed
by cosine law as
2 2 2
𝐵𝐶 = 𝐴𝐶 + 𝐴𝐵 − 2(𝐴𝐶)(𝐴𝐵) cos 𝑐𝑜𝑠 𝐴
b. After the interior angle at point A is determined, compute the rest of the interior
angle of the triangle, following the same formula.
c. A similar procedure of computation is continued until the interior angle at point E
(the check base) is determined.
d. Compute the exterior angle at point E.
5. Determining Relative Precision:
a. Determine the difference between the measured exterior angle and the computed
exterior angle at point E.
b. Divide the difference by the measured exterior angle and reduce the numerator to
unity to determine the relative precision
