Rafters…Geometry

Standard

So, my dad is building a storage building.  This is the design he is using with end dimensions for his project.

image

Easyrafters.com

He asks, “Can your students help me figure out the pitch of the roof? How long should I cut the rafters?  What angles do I use?”

Truth is, my dad likely already has them cut, ready to put together, but he knows there’s a bit of math involved that I might enjoy sharing with my class.

As I read the descritpion, I see this style is a regular octagon. 360° / 8 = 45°.  So the interior angle will be 135°.

When you cut your wood, do I split that angle in half?

I shared the diagram with other geometry teachers and Mr. H, our Carpentry Instructor at LC Area Technology Center.   I wanted to use the right approach/vocabulary Mr. H uses in his courses.  He replied almost immediately. 
The plan is to visit his classroom/shop area soon.

Now, how can I make this real for my students?  Thinking if I give them enough supplies, aka strips of construction paper to model planks of wood, and allow them to create an accurate model, describing processes for finding rafter lengths and angle measures.  Does that make sense?

An opportunity for some use of Trig, or at least a reason to use trig outside the classroom.

The website dad shared has different designs of rafters…which means we have a bank of problems to pull from.

A comment from Mr. H in our back and forth emails…

…one of the hardest to teach…geometry uses what I call the “back angle” measurement (I interpret as interior angle) and carpentry we use the “smaller” angle because we make the cuts at the intersections (if that makes sense)

.

Mr. H shared some online tools and resources as well to explore.
http://www.blocklayer.com/Roof/GambrelEng.aspx

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