In the preparation for the Geodetic Engineering Licensure Examination, the BSGE students must memorized the fastest possible solution for the TRIANGULATION ADJUSTMENT using casio fx-991 es plus calculator technique in order to save time during the said examination. note: lec 2 and above wala akong nilagay na solution para hindi makupya techniques ko. just add me on fb para ituro ko sa inyo solution. Kasi itong solution ko wala sa google, youtube, calc tech books at hindi rin itinuro sa review center.

1. ENGR. BRODDETT B. ABATAYO, GE, REA
Part-time Lecturer – GE division, CEIT, CSU, Ampayon, Butuan City
Research Assistant – Phil-LiDAR 2 Project, CSU, Ampayon, Butuan City
Proprietor – BPA ABATAYO Land Surveying Services
1
with CASIO fx-991 es plus Calculator Technique
Lecture 4
Caraga State University
College of Engineering and Information Technology
Ampayon, Butuan City 8600
TRIANGULATION
ADJUSTMENT
GE 105 – Theory of Errors and Adjustments

2. HORIZONTAL CONTROL SURVEY
TRAVERSE
TRILATERATION (SIDE)
TRIANGULATION (ANGLE)

3. TRIANGULATION FIGURES
CHAIN OF TRIANGLES
CHAIN OF QUADRILATERALS
CHAIN OF POLYGONS

4. TRIANGULATION FIGURES
Chain of Triangles

5. TRIANGULATION FIGURES
Chain of Quadrilaterals

6. TRIANGULATION FIGURES
Chain of Polygons

7. TRIANGULATION ADJUSTMENT
a. The sum of the angles about each station is equals to 360°.
CHAIN OF TRIANGLES
Step 1: STATION ADJUSTMENT
Step 2: FIGURE ADJUSTMENT
b. The sum of the interior angles of each triangle equals to 180°.

8. Angle
Measured
Value
Station
Adjustment
Figure
Adjustment
A 312°00‘24"
B 47°59‘40"
C 137°10‘29"
D 57°02‘42"
E 100°40‘25"
F 65°06‘20"
G 241°05‘13"
H 66°53‘30"
I 52°10‘20"
J 289°00‘30"
K 70°59‘30"
L 280°43‘58"
M 27°18‘12"
N 51°57‘53"
1. Adjust the angles by station adjustment method.
TRIANGULATION ADJUSTMENT
NM
L
K
J
I
H
G
F
E
D
C
B
A
2. Adjust the angles by figure adjustment method.

9. Angle
Measured
Value
Station
Adjustment
Figure
Adjustment
A 312°00‘24" 312°00‘22"
B 47°59‘40" 47°59‘38"
C 137°10‘29" 137°10‘30"
D 57°02‘42" 57°02‘43"
E 100°40‘25" 100°40‘26"
F 65°06‘20" 65°06‘21"
G 241°05‘13" 241°02‘12"
H 66°53‘30" 66°50’29"
I 52°10‘20" 52°07‘19"
J 289°00‘30" 289°00‘30"
K 70°59‘30" 70°59‘30"
L 280°43‘58" 280°43‘57"
M 27°18‘12" 27°18‘11"
N 51°57‘53" 51°57‘52"
1. Adjust the angles by station adjustment method.
TRIANGULATION ADJUSTMENT
NM
L
K
J
I
H
G
F
E
D
C
B
A
2. Adjust the angles by figure adjustment method.

10. Angle
Measured
Value
Station
Adjustment
Figure
Adjustment
A 312°00‘24" 312°00‘22"
B 47°59‘40" 47°59‘38" 48°00’48.67"
C 137°10‘29" 137°10‘30"
D 57°02‘42" 57°02‘43" 57°02’41.33"
E 100°40‘25" 100°40‘26" 100°38’27.33"
F 65°06‘20" 65°06‘21" 65°07’31.67"
G 241°05‘13" 241°02‘12"
H 66°53‘30" 66°50’29" 66°51’39.67"
I 52°10‘20" 52°07‘19" 52°05’20.33"
J 289°00‘30" 289°00‘30"
K 70°59‘30" 70°59‘30" 70°59’28.33"
L 280°43‘58" 280°43‘57"
M 27°18‘12" 27°18‘11" 27°16’12.33"
N 51°57‘53" 51°57‘52" 51°57’50.33"
1. Adjust the angles by station adjustment method.
TRIANGULATION ADJUSTMENT
2. Adjust the angles by figure adjustment method.
NM
L
K
J
I
H
G
F
E
D
C
B
A

11. TRIANGULATION ADJUSTMENT
a. Sum of angles about each station is equal to 360°.
CHAIN OF QUADRILATERAL
Step 1: STATION ADJUSTMENT
A: ANGLE CONDITION
Step 2: FIGURE ADJUSTMENT
a. The sine of each angle should be proportional to the length of
the opposite side of that triangle.
B: SIDE CONDITION
a. Sum of interior angles equals to 360°.
b. Opposite angles at the intersection of diagonals should be equal.

12. 1. Adjust the angles by simple adjustment method.
TRIANGULATION ADJUSTMENT
F
G
H
A B
C
D
E
Angle Value
A 42°38‘36"
B 64°52‘28"
C 40°32‘57"
D 31°56‘07"
E 62°00‘46"
F 45°29‘58"
G 33°31‘32"
H 38°57‘40"

13. F
G
H
A B
C
D
E
Angle Value
ANGLE CONDITION
SIDE CONDITIONFigure Adjustment
(Step 2 a)
Figure Adjustment
(Step 2 b)
A 42°38‘36"
B 64°52‘28"
C 40°32‘57"
D 31°56‘07"
E 62°00‘46"
F 45°29‘58"
G 33°31‘32"
H 38°57‘40"

14. F
G
H
A B
C
D
E
Angle Value
ANGLE CONDITION
SIDE CONDITIONFigure Adjustment
(Step 2 a)
Figure Adjustment
(Step 2 b)
A 42°38‘36" 42°38’35.5"
B 64°52‘28" 64°52’27.5"
C 40°32‘57" 40°32’56.5"
D 31°56‘07" 31°56’06.5"
E 62°00‘46" 62°00’45.5"
F 45°29‘58" 45°29’57.5"
G 33°31‘32" 33°31’31.5"
H 38°57‘40" 38°57’39.5"

15. F
G
H
A B
C
D
E
Angle Value
ANGLE CONDITION
SIDE CONDITIONFigure Adjustment
(Step 2 a)
Figure Adjustment
(Step 2 b)
A 42°38‘36" 42°38’35.5" 42°38’30.5"
B 64°52‘28" 64°52’27.5" 64°52’22.5"
C 40°32‘57" 40°32’56.5" 40°32’58.5"
D 31°56‘07" 31°56’06.5" 31°56’08.5"
E 62°00‘46" 62°00’45.5" 62°00’50.5"
F 45°29‘58" 45°29’57.5" 45°30’02.5"
G 33°31‘32" 33°31’31.5" 33°31’29.5"
H 38°57‘40" 38°57’39.5" 38°57’37.5"

16. F
G
H
A B
C
D
E
Angle Value
ANGLE CONDITION
SIDE CONDITIONFigure Adjustment
(Step 2 a)
Figure Adjustment
(Step 2 b)
A 42°38‘36" 42°38’35.5" 42°38’30.5" 42°38’30.45"
B 64°52‘28" 64°52’27.5" 64°52’22.5" 64°52’22.55"
C 40°32‘57" 40°32’56.5" 40°32’58.5" 40°32’58.45"
D 31°56‘07" 31°56’06.5" 31°56’08.5" 31°56’08.55"
E 62°00‘46" 62°00’45.5" 62°00’50.5" 62°00’50.45"
F 45°29‘58" 45°29’57.5" 45°30’02.5" 45°30’02.55"
G 33°31‘32" 33°31’31.5" 33°31’29.5" 33°31’29.45"
H 38°57‘40" 38°57’39.5" 38°57’37.5" 38°57’37.55"