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7 ANGLES, AZIMUTHS, AND BEARINGS
Asterisks indicate problems that have partial answers given in Appendix G.
7.1 Define the different reference meridians that can be used for the direction of a line.
7.2 List the three basic requirements in determining an angle.
7.3 Why is it important to adopt a standard angle measuring procedure, such as always
measuring angles to the right?
7.4 What is the relationship of a forward and back azimuth?
See Section 7.5, paragraph 2: “A line’s forward direction can be given by its forward
7.5 Convert: *(a)
203 26 48
to grads (b) 1.789546 radians to degrees, minutes, and
seconds (c) 156°07′34″ to radians.
(*)
© 2018 Pearson Education, Inc., Hoboken, NJ. All rights reserved. This material is protected under all
7.6 65°26′37″,127°25′46″,254°23′07″,and 295°14′08″
Bearings
Angles
N65°26’37”E
61°59’09”
S52°34’14”E
126°57’21”
S74°23’07”W
40°51’01”
N64°45’52”W
130°12’29”
7.7 87°08′04″,165°44′58″,203°16′38″,and 313°59′02″
7.8 N36°17′54″E, S78°13′15″E, S52°34′09″W, and N67°23′14″W
Azimuths
Angles
36°17’54”
65°28’51”
101°46’45”
130°47’24”
232°34’09”
60°02’37”
292°36’46”
103°41’08”
7.9 N88°05′23″E, S23°56′23″E, S44°00′48″W, and N14°24′44″W
Azimuths
Angles
88°05’23”
67°58’14”
156°03’37”
67°57’11”
224°00’48”
121°34’28”
345°35’16”
102°30’07”
Compute the azimuth from north of line CD in Problems 7.10 through 7.12. (Azimuths of AB
are also from north.)
*7.10 Azimuth 𝐴B = 101°26′32″; angles to the right 𝐴𝐵𝐶 = 50°54′26″, 𝐵𝐶𝐷 =
Bearings
Angles
© 2018 Pearson Education, Inc., Hoboken, NJ. All rights reserved. This material is protected under all
copyright laws as they currently exist. No portion of this material may be reproduced, in any form
or by any means, without permission in writing from the publisher.
7.11 Bearing 𝐴𝐵 = S23°08′24″W; angles to the right 𝐴𝐵𝐶 = 98°20′06″, 𝐵𝐶𝐷 =
7.12 AzimuthAB 343°26′14″; angles to the right 𝐴𝐵𝐶 = 66°36′10″, 𝐵𝐶𝐷 = 82°16′24″.
*7.13 For a bearing
08 53 56 WDE N
and angles to the right, compute the bearing of FG
if angle
88 12 29 and 40 20 30 .DEF EFG
7.14 Similar to Problem 7.13, except the azimuth of DE is 85°58′06″ and angles to the right
DEF and EFG are 21°44′52″ and 86°10′14″, respectively.
7.15 𝐴 = 82°13′15″, 𝐵 = 116°35′18″, 𝐶 = 28°45′22″, 𝐷 = 195°16′28″, 𝐸 =
117°09′37"
Course
Bearing
Azimuth
AB
Due North
0°00'00"
BC
N63°24'42"W
296°35'18"
CD
S34°39'20"E
145°20'40"
DE
S19°22'52"E
160°37'08"
EA
S82°13'15"E
97°46’45"
*7.16 𝐴 = 90°29′18″, 𝐵 = 107°54′36″, 𝐶 = 104°06′37″, 𝐷 = 129°02′57″, 𝐸 = 108°26′32″
Course
Bearing
Azimuth
AB
Due North
0°00'00"
BC
N72°05'24"W
287°54'36"
CD
S32°01'13"W
212°01'13"
DE
S18°55'50"E
161°04'10"
EA
N89°30'42"
89°30'42"
7.17 𝐴 = 156°23′53″, 𝐵 = 53°36′08″, 𝐶 = 83°15′58", 𝐷 = 153°52′00″, 𝐸 = 92°52′01″
Course
Bearing
Azimuth
AB
Due North
0°00'00"
BC
S53°36'08"W
233°36'08"
CD
S43°07'54"E
136°52'06"
DE
S69°15'54"E
110°44'06"
EA
N23°36'07"E
23°36'07"
© 2018 Pearson Education, Inc., Hoboken, NJ. All rights reserved. This material is protected under all
copyright laws as they currently exist. No portion of this material may be reproduced, in any form
or by any means, without permission in writing from the publisher.
7.18 Bearing of 𝐴𝐵 = 45°04′20″ (Station C is westerly from B.)
Course
Azimuths
AB
45°04'20"
BC
345°04'20"
CD
285°04'20"
DE
225°04'20"
EF
165°04'20"
FA
105°04'20"
7.19 Azimuth of 𝐴𝐵 = 303°16′22″ (Station C is westerly from B.)
Course
Azimuths
AB
303°16'22"
BC
243°16'22"
CD
183°16’22"
DE
123°16'22"
EF
63°16'22"
FA
3°16'22"
7.20 Azimuth of 𝐴𝐵 =256°23′50″ (Station C is westerly from B.)
Course
Azimuths
AB
256°23'50"
BC
196°23'50"
CD
136°23'50"
DE
76°23'50"
EF
16°23'50"
FA
316°23'50"
7.21 Bearing 𝐴𝐵 = 𝑁1°43′22″𝑊.
Course
Azimuths
AB
358°16'38"
BC
256°37'06"
CD
168°47'38"
DA
69°54'40"
7.22 Azimuth 𝐴𝐵 =96°10′20″.
© 2018 Pearson Education, Inc., Hoboken, NJ. All rights reserved. This material is protected under all
Course
Azimuths
AB
96°10'20"
BC
354°30'48"
CD
266°41'20"
DA
167°48'22"
7.23 Similar to Problem 7.21, except that bearings are required, and fixed bearing 𝐵 =
S44°46′25″W.
Course
Bearings
AB
S44°46’25”W
BC
S56°53'07"E
CD
N35°17'25"E
DA
N63°35'33"W
7.24 Similar to Problem 7.22, except that bearings are required, and fixed azimuth 𝐵 =
106°48′29″ (from north).
Course
Bearings
AB
S73°11'21"E
BC
N5°09'07"E
CD
N82°40'21"W
DA
S1°33'19"E
7.25 Geometrically show how the sum of the interior angles of a pentagon
(five sides) can be computed using the formula (𝑛 − 2)180°?
7.26 Determine the predicted declinations on January 1, 2019 using the
WMM 2015 model at the following locations.
latitude 42 58 28 N, longitude 77 12 36 W, elevation 310.0 m;
(b)
latitude 37 56 44 N,longitude 110 50 40 W,elevation 1500m;
10.5°E
latitude 41 1815 N,longitude 76 00 26 W,elevation 240m
7.27 Using Table 7.4, what is the predicted total difference in magnetic declination between
Boston, MA and Seattle, WA on January 1, 2019?
7.28 The magnetic declination at a certain place is 8°15′E. What is the magnetic bearing
there: (a) of true north (b) of true south (c) of true east?
7.29 Same as Problem 7.28, except the magnetic declination at the place is 14°50′W.
