Discovering SOHCAHTOA

'An investigation to discover the 3 trigonometric ratios using dynamic geometry software'

This investigation will help you learn how to find unknown sides in right-angled triangles.  Trigonometry (comes from Greek “trigonon” meaning triangle and “metria” meaning measurement).  Trigonometry is hugely important in surveying.  You may have seen surveyors using this funny looking instrument in this picture.  What are they doing? They are measuring land.  It is rather difficult to measure lengths especially when the ground is difficult, but it is easy to measure angles to a very high degree of accuracy.  They make a careful measurement of a distance between two specific places then build up a series of triangles and use trigonometry to measure lengths.  The whole process is called triangulation, and is used to measure building sites, national parks, countries and even whole continents!


  • This activity is an investigation.
  • Students start with pencil and paper to get to grips with similar triangles then they use a dynamic geometry package (Geogebra) to generate right angled triangles and measure their lengths.
  • The use of dynamic geometry software enables this introduction to trigonometry to move on quickly.  Students need access to a computer but the software does not need to be installed.
  • Students discover that the sine, cosine and tangent buttons on their calculators equate to these ratios. 
  • The students can work individually but sharing of results is essential.
  • A recap of similar triangles may be useful beforehand.
  • This activity can be delivered in 90 to 120 minutes depending on the ability of the students.
  • Neither students (nor teachers) need have had any prior experience of this software package.


Here is the worksheet for discovering ratios in right angled triangles

Here is the first Geogebra manipulative to investigate the opposite and hypotenuse

Here is the second Geogebra manipulative for investigating Cosine and Tangent

Teachers may wish to read the following notes  Discovering SOHCAHTOA

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