Computing bearings from a starting bearing and an observed angle

204 Pages·2009·4.98 MB·English

SURVEYING COMPUTATIONS
CPPSIS3010A
CPPSIS4011A
Learner’s Guide
BC1091
CPPSIS3010A
CPPSIS4011A
Surveying Computations
Learner’s Guide
Copyright and Terms of Use
© Department of Training and Workforce Development 2016 (unless indicated
otherwise, for example ‘Excluded Material’).
The copyright material published in this product is subject to the Copyright Act 1968
(Cth), and is owned by the Department of Training and Workforce Development or,
where indicated, by a party other than the Department of Training and Workforce
Development. The Department of Training and Workforce Development supports
and encourages use of its material for all legitimate purposes.
Copyright material available on this website is licensed under a Creative Commons
Attribution 4.0 (CC BY 4.0) license unless indicated otherwise (Excluded Material).

Except in relation to Excluded Material this license allows you to:
 Share — copy and redistribute the material in any medium or format
 Adapt — remix, transform, and build upon the material for any purpose, even
commercially
provided you attribute the Department of Training and Workforce Development as
the source of the copyright material. The Department of Training and Workforce
Development requests attribution as: © Department of Training and Workforce
Development (year of publication).
Excluded Material not available under a Creative Commons license:
1. The Department of Training and Workforce Development logo, other logos and
trademark protected material; and
2. Material owned by third parties that has been reproduced with permission.
Permission will need to be obtained from third parties to re-use their material.
Excluded Material may not be licensed under a CC BY license and can only be used
in accordance with the specific terms of use attached to that material or where
permitted by the Copyright Act 1968 (Cth). If you want to use such material in a
manner that is not covered by those specific terms of use, you must request
permission from the copyright owner of the material.
If you have any questions regarding use of material available in this product, please
contact the Department of Training and Workforce Development.
Training Sector Services
Telephone: [phone]
Email: [email protected]
Website: www.dtwd.wa.gov.au
First published 2009
Updated May 2014
ISBN 978-1-74205-268-7
© WestOne Services 2009
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
system or transmitted in any form or by any means, electronic, mechanical, photocopying,
recording or otherwise, without the prior written permission of WestOne Services.
Whilst every effort has been made to ensure the accuracy of the information contained
in this publication, no guarantee can be given that all errors and omissions have been
excluded. No responsibility for loss occasioned to any person acting or refraining from
action as a result of the material in this publication can be accepted by WestOne Services.
Published by and available from
WestOne Services
1 Prospect Place West Perth WA 6005
Tel: [phone] Fax: [phone]
Email: [email protected]
Website: www.westone.wa.gov.au
This product contains various images © Jupiter Images 2009, used under licence.
Surveying Computations
Contents
Introduction 7
Chapter 1 Scientific notation; transformation of formulae ..............................9
1.1 Scientifi c notation .................................................................................................9
1.2 Equation transformation .....................................................................................11
Chapter 2 Trigonometric functions ..................................................................17
2.1 Angles ................................................................................................................17
2.2 Coordinate axes ..................................................................................................18
2.3 Sine and cosine ...................................................................................................20
2.4 Tangents .............................................................................................................23
2.5 Inverse trigonometric functions .........................................................................26
2.6 Domain of angles ...............................................................................................27
2.7 The reciprocal trigonometric functions (cosec, sec, cot) ...................................34
Chapter 3 Right-angled triangles .....................................................................35
3.1 Introduction ........................................................................................................35
3.2 Sin and cos functions .........................................................................................36
3.3 Tan functions ......................................................................................................37
3.4 Pythagoras’ theorem ...........................................................................................38
3.5 Areas ..................................................................................................................38
Chapter 4 Scalene triangles ..............................................................................43
4.1 Elements .............................................................................................................43
4.2 Sine rule, cosine rule and the area formula ........................................................45
4.3 Loss of precision when computing angles from lengths ....................................50
4.4 Using the formulae .............................................................................................53
4.5 Special situations ................................................................................................60
4.6 Applications .......................................................................................................63
4.7 Solving triangles when area is given ..................................................................69
3
Chapter 5 Angles and bearings ........................................................................75
5.1 Angles ................................................................................................................75
5.2 Bearings ..............................................................................................................77
Chapter 6 Distance, line definition (polar coordinates), point definition,
(rectangular coordinates) ...............................................................89
6.1 Distance ..............................................................................................................89
6.2 Line defi nition (polar coordinates) .....................................................................90
6.3 Point defi nition ...................................................................................................92
6.4 The relationship between line defi nition and rectangular coordinates of
end points of a line .............................................................................................94
6.5 Calculators: use of rectangular→polar (R→P) function key ...............................106
Chapter 7 Vectors ............................................................................................107
7.1 N and E as the components of a vector .......................................................108
7.2 Vectors in surveying – summing vectors to prove a survey ...................................110
Chapter 8 Adjustment of misclose in closed traverses ...............................115
8.1 Traverse surveying ..................................................................................................115
8.2 Traverse closure ......................................................................................................116
8.3 Misclose ..................................................................................................................117
8.4 Angular misclose ....................................................................................................119
8.5 Linear misclose and adjustment ..............................................................................127
Chapter 9 Areas of polygons ..........................................................................143
9.1 Areas of regular rectilinear figures .........................................................................143
9.2 Areas of polygons ...................................................................................................146
9.3 Calculating area using coordinates .........................................................................146
Chapter 10 Missing measurements .................................................................151
10.1 Summing vectors to prove a survey ........................................................................151
10.2 The sum, difference and translation of vectors .......................................................152
10.3 Closing vectors .......................................................................................................153
10.4 Partially defined vectors .........................................................................................153
10.5 Missing vectors .......................................................................................................154
10.6 Calculating missing measurements .........................................................................158
4
Surveying Computations
Chapter 11 Simple circular curves ...................................................................175
11.1 Introduction .............................................................................................................175
11.2 The geometry of curves ..........................................................................................175
11.3 Elements of simple circular curves .........................................................................180
11.4 Derived formulae ....................................................................................................181
11.5 Areas .......................................................................................................................184
Chapter 12 Roads ..............................................................................................189
12.1 Introduction .............................................................................................................189
12.2 Single-width roads ..................................................................................................190
12.3 Computations relating to roads ...............................................................................194
Appendix A Calculator requirements ................................................................199
5
6
SSuurrvveeyyiinngg CCoommppuuttaattiioonnss
Introduction
This resource is designed to help you develop an understanding of the mathematical principles
and methods commonly used in surveying, in particular the knowledge and skills related to the
following units of competency.
CPPSIS3010A – Perform basic spatial computations
CPPSIS4011A – Perform surveying computations
The resource is divided into chapters. At the end of each chapter, you will be required to
complete set activities in your tutorial book to practice knowledge and methods discussed in
each chapter.
You will require a scientific calculator. For more information, please see the Appendix A –
Calculator requirements at the back of this Learner’s Guide.
77
Introduction
88