Trigonometry for Engineering Technology

With Mechanical, Civil, and Architectural Applications

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Trigonometry for Engineering Technology

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Trigonometry for Engineering Technology

With Mechanical, Civil, and Architectural Applications

Gary Powers


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Trigonometry for Engineering Technology teaches the fundamentals or right angle trigonometry while also placing strong emphasis on examples from the field of engineering technology. Written for those without prior experience in the subject, as well as those who need a refresher, its intent is to engage students in a topic that many might otherwise consider unimportant in a future career. May also be found useful by manufacturing companies with in-house training programs.



  • Emphasizes examples from the fields of engineering technology for students who are studying to prepare for work in those fields
  • Many examples and exercises include illustrations to enhance the explanation of real-world scenarios
  • Each chapter includes example problems that demonstrate a problem-solving procedure for specific problem types. The example problems are followed by exercises that the students solve for practice
  • Several chapters are included to supplement the right angle trigonometry topics, including Law of Sines, Law of Cosines, and graphing trigonometry functions
  • An open format allows students to use the text as a workbook in class and during study
  • Includes answers and solutions to exercise


Gary Powers has taught a wide range of classes for more than 15 years at South Hills School of Business and Technology, a two-year, post-secondary school located in State College, PA., including Geometry, Trigonometry, Physics, Dimensional Metrology, Machining, CNC Programming, and Mechanical Design. His students regularly serve internships with and are hired by a variety of engineering and manufacturing firms. Previously, Gary was employed for 16 years by Corning, Inc. as a manufacturing supervisor and process engineer. He holds a B.S. in Aerospace Engineering from the U.S. Naval Academy, and after graduating from the Naval Nuclear Power School he served in the submarine force. Gary is a member of the American Society of Engineering Education.

Chapter 8 Mechanical Applications


Angularity Measurement with a Sine Bar


Some mechanical parts may have a surface that is angled to the rest of the part. An example of this is shown in Figure 8.3.


There are several methods for specifying the tolerance of this angle. One method is to use the basic angle-tolerance which is shown in the title block as +/- 0° 15'. A basic angle tolerance is measured directly using a bevel protractor.


If the tolerance must be much closer than a basic angle tolerance, then an angularity tolerance can be specified as shown in Figure 8,3. Angularity is part of a tolerancing system called Geometric Dimensioning and Tolerancing (GD&T). If an angularity tolerance is specified, it takes precedence over the basic angle tolerance shown in the title block of the drawing.


In Figure 8.3, the angularity tolerance is shown as .003 in. The angularity is referenced to surface A, which is labeled as the bottom surface of the part. An angle must be referenced to another feature on a part...


Figure 8.3 Measurement with a sine bar

  • Introduction
  • Angles
  • Triangles
  • Preparation for Right Angle Trigonometry
  • Practice Worksheets for Chapters 2 – 4
  • Functions of Trigonometry
  • Solving for Unknown Sides
  • Solving for Unknown Angles
  • Practice Worksheets for Chapters 6 – 7
  • Mechanical Applications
  • Practice Worksheet for Chapter 8
  • Civil Applications
  • Practice Worksheet for Chapter 9
  • Architectural and Construction Applications
  • Practice Worksheet for Chapter 10
  • Graphing Trigonometry Functions
  • Law of Sines
  • Law of Cosines
  • Practice Worksheet for Chapters 11 – 13
  • Appendix: Exercise Answers and Solutions