Topic 1-Bearing and Angle

TOPIC 1

BEARING AND ANGLE

SYURINA BINTI SAMSUDIN

Pensyarah
Jabatan Kejuruteraan Awam
Politeknik Sultan Haji Ahmad Shah

Determine bearing and angle conversion TOPIC AND SUB
TOPIC
Differentiate between terms of bearing and angle

Differentiate between terms of bearing and whole circle
bearing

Compute whole circle bearing conversion to quadrant
bearing

Calculate the internal angle from two bearings

Calculate the bearing from internal angle and a known bearing

FIRSTUP 2
CONSULTANTS

DIFFERENTIATE BETWEEN
TERMS OF BEARING AND
ANGLE

FIRSTUP 3
CONSULTANTS

Bearing Angle

Angle from true north Different of 2 bearing

Example angle for ∡ABC

Quadrant IV Quadrant I

Quadrant III Quadrant II

Forward bearing A to B is 58° 26’ 35”
Back bearing B to A is 58° 26’ 35” + 180° = 238° 26’ 35”

Forward bearing B to C is 109° 37’ 55”

Back Bearing from C to B is 109° 37’ 55” + 180° = 289° 37’ 55” FIRSTUP

CONSULTANTS 4

Whole Circle bearing Quadrant Bearing
[WCB]
angle lying between 0˚
clockwise angle from to 900
0˚ to 360˚
direction from north or
south

Quadrant IV Quadrant I
2700-3600 00-900

1800-2700 900-1800
Quadrant III Quadrant II

FIRSTUP 5
CONSULTANTS

COMPUTE WHOLE CIRCLE
BEARING CONVERSION TO

QUADRANT BEARING

FIRSTUP 6
CONSULTANTS

MUST BE REMEMBERED

Diagram Whole Circle Bearing Quadrant Bearing
N θ° E
θ°
Value must between 00-

900

Value must between 00- S θ° E

1800 = S (180° - a° ) E

a = 180° - θ°
a

FIRSTUP 7
CONSULTANTS

MUST BE REMEMBERED CONT.…..

Diagram Whole Circle Bearing Quadrant Bearing

θ° S θ° W
Value must between 00- = S (a - 180 ) W

2700

= 180 + 
a

Value must between N θ° W

2700-3600 = N (360° - a°) W
a = 360 - 

FIRSTUP 8
CONSULTANTS

EXAMPLE 1 : Convert Quadrant Bearing To Whole Circle Bearing

Diagram Quadrant Bearing Whole Circle
Bearing

Question: Answer :
N 70° 35’ 40” E 70° 35’ 40”

Question: Answer:
N 35° 45’ 23” W = 360° - 35° 45’ 23”

= 324° 14’ 37”

FIRSTUP 9
CONSULTANTS

EXAMPLE 1 CONT.. : Convert Quadrant Bearing To Whole Circle Bearing

Diagram Quadrant Bearing Whole Circle
Bearing
Question:
S 40° 37’ 30” E Answer :
_________________

You can Try It

Question: Answer:
S 40° 37’ 30” W _________________

You can Try It

FIRSTUP 10
CONSULTANTS

EXAMPLE 2 : CONVERT WHOLE CIRCLE BEARING TO QUADRANT BEARING

Diagram Whole Circle Bearing Quadrant Bearing

Question: Answer :
70° 35’ 40” N 70° 35’ 40” E

Question: Answer:
135° 45’ 23” S 44° 14’ 37” E

FIRSTUP 11
CONSULTANTS

EXAMPLE 2 CONT... : CONVERT WHOLE CIRCLE BEARING TO QUADRANT
BEARING

Diagram Whole Circle Bearing Quadrant Bearing

Question: Answer :
240° 37’ 30” _________________

You can Try It

Question: Answer:
340° 37’ 30” ________________

You can Try It

FIRSTUP 12
CONSULTANTS

CALCULATE THE
INTERNAL ANGLE FROM

TWO BEARINGS

FIRSTUP 13
CONSULTANTS

EXAMPLE 1 :

Note:
1. Check value for each bearing
2. + 180° to get right value

Angle y = 135° 34’ 54” - 39° 06’ 41”
=96° 28’ 13”

EXAMPLE 2 :

Anticlockwise, so to calculate bearing
= given bearing - angle

Angle y = 129° 53’ 12” - (237° 26’ 19” - 180°)
= 129° 53’ 12” - 57° 26’ 19”

FIRSTUP 14
CONSULTANTS

EXAMPLE 3 :

Calculate angle θ1 = 360: - 289: 23’ 22”
= 70: 36’ 38”

Calculate angle θ2 = 49: 43’ 26”

Angle y = θ1+ θ2= 70: 36’ 38” + 49: 43’ 26”
= 120: 20’ 04”

FIRSTUP 15
CONSULTANTS

CALCULATE THE BEARING
FROM INTERNAL ANGLE
AND A KNOWN BEARING

FIRSTUP 16
CONSULTANTS

EXAMPLE 1 :

Bearing x to q = 43° 42’ 08” + 78° 38’ 51”
= 122° 20’ 59”

EXAMPLE 2 :

Bearing x to q = 74°02’ 07” – (360° - 305° 12’ 21” )
= 19° 14’ 28”

FIRSTUP 17
CONSULTANTS

EXAMPLE 3:

Bearing x to q = (317° 54’ 05” -180° ) + 80° 31’
20” = 137° 54’ 05” + 80° 31’ 20”
= 218° 25’ 25”

EXAMPLE 4 :

Bearing x to q = 214° 43’ 25” – (360° -235° 16’ 35” )
= 90° 00’ 00”

FIRSTUP 18
CONSULTANTS

ASSIGNMENT 1

Figure 1.17 shows an open trash. Bering for the shortcut line is as
follows:

Bering AB = 176 18 30
Bering BC = 085 13 40
Bering CD = 153 14 30

Questions: Calculate Angle () and ()

Try to answer…….

FIRSTUP 19
CONSULTANTS

THANK YOU

FIRSTUP 20
CONSULTANTS