Some Geometry books have a chapter on Trigonometry, and in those books the applications of trig are mentioned. One of the most common applications of right triangle trigonometry is indirect measurement. A frequently used example is finding the height of a cliff, building or tree that is too tall to be directly measured.
In this project, the students use right triangle trigonometry to find the height of a tree, and then do a presentation on poster board showing their work. Students like to do projects, and are quite proud to show off the product of their work.
Materials Needed: railroad board (or thin illustration board), protractors, rulers or tape measures, drinking straws, colored pens or pencils.
This works best with students working in groups of 3. One student is the "Geometer", using the protractor to measure angles, a second student is the "Surveyor", using a ruler or tape measure to measure distances, and a third student is the "Recorder" recording the data. Each group should go outside and choose a tall tree or building to measure using "indirect measurement". A position is decided upon, at least 25 feet from the tree, with a clear view of the top and bottom of the tree. The ground between the Geometer and the tree must be relatively level. Once the position is decided upon, the surveyor measures the exact distance and records this measurement. The Geometer stands at the chosen spot and holds the protractor and straw up at eye level, sighting the tree through the straw. (see diagram on the following page. The Surveyor stands near the Observer, checking to be sure the bottom edge of the protractor is horizontal, and reading the angle of elevation.
Using trigonometry, as shown in the diagram above, and poster below, the height of the tree or building can be obtained. This is, of course, only an approximation because of the equipment and other variables involved, but it does give students hands-on experience of a true application of Mathematics.
Where there is matter,
there is geometry.
(Ubi materia, ibi geometria.)
J. Koenderink