Trigonometry: sextant and GeoGebra
Benito Bua Ares is one of our Xplora teachers. He teaches mathematics in a secondary school in Galicia, Spain and in this article he tells us more about angles and trigonometry. He also presents some projects which have been carried out by his students using open source softwares.
Angle is one important maths magnitude: in fact we need angles to work. We can do examples and exercises giving angles like a known data or we can also measure angles with a graduate circle on a sheet of paper but if we want to solve real problems outside the classroom, we need an instrument to measure angles. There are several options to measure a vertical or horizontal angle. A tachimeter is a professional instrument to measure angles and distances, but it is very expensive.
We have also an interesting option: make and use a handmade instrument. There are some options for handmade instruments to measure angles but perhaps the best one is a sextant. It has been used by sailors and airmen until recently.
You can download the method to create and use a sextant at:
One important part of a sextant is the limbo, a graduated circle with marks for each degree: from the same website you can download also a limbo.
A limbo, which contains only the marks of each degree. After graduating the sextant, the number of degrees could be assigned to the marks.
Using GeoGebra or Geonext in trigonometry problems
To explain trigonometry concepts, you can use GeoGebra or Geonext softwares. They are GPL open source programs and they have been included in the Xplora-Knoppix DVD.
Two Galician-Spanish students aged 17, Sandra Dios, and Noelia Moraña, have carried out a nice project, measuring the area of an irregular land and using Geogebra, one of these two softwares.
They used a sextant and a metric tape to measure angles and lengths. To draw the graphics and check results, they have used GeoGebra, learning it in one 50 minutes class. The project was a voluntary task for their homework
Download the complete project. (pdf, in English)
This is what they have told about their experience: “It was a very interesting project, not only because we were able to calculate the area of the land, but also because this project has helped us to understand how trigonometry could be used in daily life.
Using a sextant to measure angles was a new experience for us and not very difficult. In fact the graphics were easier with the help of the computer programme “GeoGebra”.
This project has allowed us to improve our mathematics knowledge and to be more confident about ourselves when having to do calculations.”
Read more about Geogebra: