Math Mondays: Raising the Roof with Trigonometry

Trigonometry is covered over three units in my Precalculus class. In the first unit we work on graphing trigonometry and trigonometric functions.  The second trigonometry unit includes such topics of angles of depression and elevation, identities and the law of sines and cosines. The final trigonometry unit works with vectors.  

Some students come from Algebra 2 familiar with the basic trigonometric functions; others have not yet seen trigonometry.  This unit is a mix of review and basic trigonometry.  It is a great place for an open-ended project that taps into students’ creativity. 


I like to look for real-world applications when designing projects. For trigonometry we often work with navigation.  We will be doing quite a bit of applications with navigation when we get to vectors, so I wanted something different for this first unit.  Through discussions with colleagues and a little research, I stumbled upon architecture as an interesting application.  

The scope of the project: Students design a building with a function of their choice (house, theater, rock climbing gym to name a few). The parameters include a sloped roof.  



I share this video to kick off the project.  I like that it both gives students an idea of one application of trigonometry and also introduces another STEM career, one that is less discussed.

  • Students design the exterior of the building and draw scale drawings.  
  • Students draw front elevations using trigonometry to determine the roof angles, length and more.  This 1-2 day project forms the primary assessment for the unit. 
  • I give a find the error assignment for graphing trigonometry functions as well (Check it out FREE here). 

If you try the roof project for your trigonometry unit:

  • Give all parts of the project at the beginning. Students can work at their own pace AND they can start thinking about their roof shape even as they design the floor plan. 
  • Have an ample supply of graph paper. This project works best on graph paper for scale and right angles. 
  • Have protractors for students.  Students use these to verify and draw angles.  
  • Have clear expected outcomes.  This is usually a mini-project in that I’m not looking for a presentation or a polished piece to be handed in.  I want to see their calculations.  The drawings must be neat and clearly labeled, but I’m not expecting color, title pages or long-written descriptions.  
This is part of a series of posts focused on teaching PreCalculus.  Topics include:

Trigonometric Functions
Applications of Trigonometry
Systems of Equations and Matrices
Analytic Geometry in 2 and 3 dimensions
Discrete Mathematics
Introducing Limits - the Calculus of PreCalculus



Math Mondays is a bi-weekly blog post (2nd and 4th Monday of each month) sharing tips, ideas, resources, and products for teaching math.  If you have questions or think there is something I should include, you can leave me a message in the comments section below or at the store in the question and answer section.

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