Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

166 Chapter 7 Length and Length-Related Parameters

was funded and controlled by the U.S. Department of Defense for military applications, it now

has millions of users. GPS navigation receivers are now common in airplanes, automobiles,

buses, cellphones, and hand-held receivers used by hikers.

Sometimes, distances or dimensions are determined indirectly using trigonometric prin-

ciples. For example, let us say that we want to determine the height of a building similar to the

one shown in Figure 7.3. but do not have access to accurate measuring devices. With a drink-

ing straw, a protractor, and a steel tape we can determine a reasonable value for the height of

the building by measuring the angle and the dimensionsdandh 1. The analysis is shown in

Figure 7.3. Note thath 1 represents the distance from the ground to the eye of a person look-

ing through the straw. The angle (alpha) is the angle between the straw, which is focused on

the edge of the roof, and a horizontal line. The protractor is used to measure the angle that the

straw makes with the horizontal line.

It is very likely that you have used trigonometric tools to analyze some problems in the past.

It is also possible that you may have not used them recently. If that is the case, then the tools

have been sitting in your mental toolbox for a while and quite possibly have collected some

rust in your head! Or you may have forgotten altogether how to properly use the tools. Because

of their importance, let us review some of these basic relationships and definitions. For a right

triangle, the Pythagorean relation may be expressed by

a

2

b

2

c

2

An example of an electronic

distance measuring

instrument used in surveying.

Source:Courtesy Pentax

Corporation

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