Surveying, GPS, Digitization - A Primer of GIS: Fundamental Geographic and Cartographic Concepts - page 155

the paper coincides with point C on the ground, and repeat the sighting with your
straightedge and drawing of a line. The two lines should meet, forming a triangle.
Help the next person set up, checking to see if he or she is also following the correct
procedure.

Now, use the protractor to determine the angles of the triangle you have just drawn.
The protractor has two degree indications. Negative angles run from left to right,
positive angles run from right to left. Use the indications that correspond to the
direction of the angle, or direction of the “base” of the angle—for example, if the
base of the angle (also called the “initial side”) points to the right, use the angle indi-
cators that run from right to left. Write the angle measurements on your worksheet
together with the figures.
You can now use the law of sines to determine the distances from the baseline to
the surveyed object. You only need to calculate one distance, but calculating both
distances will be helpful.
Repeat Steps 1, 2, and 3 for the other four objects, making sure to position your
worksheet accurately and measure angles very carefully. Put all your measures and
the results of your calculations down on your worksheet. Work together with other
people in your group to make sure everybody has the same (or almost the same)
measures.

Evaluation
When you have finished surveying and calculating distances, answer the following
questions.
Question 1: Draw a line in another color connecting your surveyed objects on your
worksheet. Does it look like a straight line approximating the wall? Compare your
measurements and calculations for each of the five objects you surveyed. How
accurate were your measurements and calculations? What is the difference between
your calculated positions and measurements? What explains the difference?
Question 2: You surveyed in only two dimensions. Would adding a third dimension
for height make your survey less accurate or more accurate? Why? What about for
more precise surveying work in general? What is the name of the process a surveyor
conducts to assure accurate height measurements?

3.

EXTENDED EXERCISE: The Law of Sines and Euclidean
Geometry

Introduction
In this exercise, you will be using Euclidean geometry, named after the ancient
Greek mathematician Euclid who lived around 300 B.C. and who wrote 13 topics
about mathematics collectively called Euclid's Elements . It is the most established
approach to codify perceptions of space and motion. Euclidean geometry is also
called “classical geometry” because many other people contributed to it and added
to it over the centuries. Euclid's geometry consists of 10 axioms for fundamental