TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS...
-
Upload
sheena-hines -
Category
Documents
-
view
215 -
download
0
Transcript of TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS...
![Page 1: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/1.jpg)
TOPIC 4ANGLE AND DIRECTION
MEASUREMENT
MS SITI KAMARIAH MD SA’ATLECTURER
SCHOOL OF BIOPROCESS [email protected]
![Page 2: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/2.jpg)
Introduction
An angle is defined as the difference in direction between two convergent lines.
![Page 3: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/3.jpg)
Types of Angles
Vertical angles Zenith angles Nadir angles
![Page 4: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/4.jpg)
Definition
A vertical angle is formed by two intersecting lines in a vertical plane, one of these lines horizontal.
A zenith angle is the complementary angle to the vertical angle and is directly above the obeserver
A Nadir angle is below the observer
![Page 5: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/5.jpg)
Three Reference Directions - Angles
![Page 6: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/6.jpg)
Meridians
A line on the mean surface of the earth joining north and south poles is called meridian.
Note: Geographic meridians are
fixed, magnetic meridians vary with time and location.
Relationship between “true” meridian and grid meridians
Figure 4.2
![Page 7: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/7.jpg)
Geographic and Grid Meridians
![Page 8: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/8.jpg)
Horizontal Angles
A horizontal angle is formed by the directions to two objects in a horizontal plane. Interior angles Exterior angles Deflection angles
![Page 9: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/9.jpg)
Closed Traverse
![Page 10: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/10.jpg)
Open Traverse
![Page 11: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/11.jpg)
Directions
Azimuth An Azimuth is the direction of a line as given by an
angle measured clockwise (usually) from the north. Azimuth range in magnitude from 0° to 360°.
Bearing Bearing is the direction of a line as given by the acute
angle between the line and a meridian. The bearing angle is always accompanied by letters
that locate the quadrant in which line falls (NE, NW, SE or SW).
![Page 12: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/12.jpg)
Azimuths
![Page 13: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/13.jpg)
Bearing
![Page 14: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/14.jpg)
Relationships Between Bearings and Azimuths
To convert from azimuths to bearing, a = azimuths b = bearing
Quadrant Angles Conversion
NE 0o 90o a = b
SE 90o 180o a = 180o – b
SW 180o 270o a = b +180o
NW 270o 360o a = 360o – b
![Page 15: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/15.jpg)
Reverse Direction
In figure 4.8 , the line AB has a bearing of N 62o 30’ E BA has a bearing of S 62o 30’ W
To reverse bearing: reverse the direction
Figure 4.7
Reverse DirectionsFigure 4.8
Reverse Bearings
Line Bearing
AB N 62o 30’ E
BA S 62o 30’ W
Line Bearing
AB N 62o 30’ E
BA S 62o 30’ W
![Page 16: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/16.jpg)
![Page 17: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/17.jpg)
Reverse Direction
CD has an azimuths of 128o 20’ DC has an azimuths of 308o 20’
To reverse azimuths: add 180o
Figure 4.8
Reverse Bearings
Line Azimuths
CD 128o 20’
DC 308o 20’
![Page 18: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/18.jpg)
Counterclockwise Direction (1)
Start
Given
![Page 19: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/19.jpg)
Counterclockwise Direction (2)
![Page 20: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/20.jpg)
Counterclockwise Direction (3)
![Page 21: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/21.jpg)
Counterclockwise Direction (4)
![Page 22: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/22.jpg)
Counterclockwise Direction (5)
Finish
Check
![Page 23: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/23.jpg)
Sketch for Azimuth Computation
![Page 24: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/24.jpg)
Clockwise Direction (1)
Start
Given
![Page 25: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/25.jpg)
Clockwise Direction (2)
![Page 26: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/26.jpg)
Clockwise Direction (3)
![Page 27: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/27.jpg)
Clockwise Direction (4)
![Page 28: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/28.jpg)
Clockwise Direction (5)
Finish
Check
![Page 29: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/29.jpg)
Start
Given
Finish
Check
![Page 30: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/30.jpg)
Azimuth Computation
When computations are to proceed around the traverse in a clockwise direction,subtract the interior angle from the back azimuth of the previous course.
When computations are to proceed around the traverse in a counter-clockwise direction, add the interior angle to the back azimuth of the previous course.
![Page 31: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/31.jpg)
Azimuths Computation
Counterclockwise direction: add the interior angle to the back azimuth of the previous course
Course Azimuths Bearing
BC 270o 28’ N 89o 32’ W
CD 209o 05’ S 29o 05’ W
DE 134o 27’ S 45o 33’ E
EA 62o 55’ N 62o 55’ E
AB 330o 00’ N 30o 00’ W
![Page 32: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/32.jpg)
Azimuths Computation
Clockwise direction: subtract the interior angle from the back azimuth of the previous course
Course Azimuths Bearing
AE 242o 55’ S 62o 55’ W
ED 314o 27’ N 45o 33’ W
DC 29o 25’ N 29o 05’ E
CB 90o 28’ S 89o 32’ E
BA 150o 00’ S 30o 00’ E
![Page 33: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/33.jpg)
Bearing Computation
Prepare a sketch showing the two traverse lines involved, with the meridian drawn through the angle station.
On the sketch, show the interior angle, the bearing angle and the required angle.
![Page 34: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/34.jpg)
Bearing Computation
Computation can proceed in a Clockwise or counterclockwise
Figure 4.11
Sketch for Bearings Computations
![Page 35: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/35.jpg)
Sketch for bearing Computation
![Page 36: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/36.jpg)
Comments on Bearing and Azimuths
Advantage of computing bearings directly from the given data in a closed traverse, is that the final computation provides a check on all the problem, ensuring the correctness of all the computed bearings
![Page 37: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/37.jpg)
Angle Measuring Equipment
Plane tables (graphical methods) Sextants Compass Tapes (or other distance measurement) Repeating instruments Directional instruments Digital theodolites and total stations
![Page 38: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/38.jpg)
Determining Angles – Taping
Need to: measure 90° angle at point X
d d
Lay off distance d either side of X
X
l l
Swing equal lengths (l)
Connect point of intersection and X
![Page 39: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/39.jpg)
Determining Angles – Taping
A
B
C
Need to: measure angle at point A
Measure distance ABMeasure distance ACMeasure distance BC
Compute angle
)AB)(AC2(
BCABACcos
222
1α
![Page 40: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/40.jpg)
Determining Angles – Taping
A
B
C
Need to: measure angle at point A
AP
PQtan 1α
Q
Lay off distance APEstablish QP AP
Measure distance QP
Compute angle
P
![Page 41: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/41.jpg)
Determining Angles – Taping
A
B
C
Need to: measure angle at point A
)AD2(
DE)sin(0.5 α
D
Lay off distance ADLay off distance AE = AD
Measure distance DE
Compute angle E
![Page 42: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/42.jpg)
Repeating Instruments
Very commonly used Characterized by
double vertical axis Three subassemblies
![Page 43: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/43.jpg)
Directional Instruments
Has single vertical axis Zero cannot be set More accurate but less
functional
![Page 44: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/44.jpg)
Total Stations
Combined measurements
Digital display
![Page 45: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/45.jpg)
Measuring Angles
Instrument handling and setup Discussed in lab
Procedure with repeating instrument
![Page 46: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/46.jpg)
Angles
All angles have three parts Backsight: The baseline or point used as zero angle. Vertex: Point where the two lines meet. Foresight: The second line or point
![Page 47: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/47.jpg)
Repetition and Centering
Repetition provides advantages Centering process
![Page 48: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/48.jpg)
“Centering”
![Page 49: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/49.jpg)
Measuring Angles
Procedure with directional instruments
Most total stations are directional instruments
![Page 50: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/50.jpg)
Angle Measuring Errors and Mistakes
Instrumental errors Natural errors Personal errors Mistakes
![Page 51: TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649d945503460f94a7bc54/html5/thumbnails/51.jpg)
THANK YOU