Without Trig, your House Would be Lopsided.

This blog post follows the "Grade of the Road" post; you'll want to read that one first.  Some of you have commented on this blog last year already (hopefully, you will remember that blog.) If you have not, take a minute to evaluate what trig function (using the angle of elevation) is the slope (or grade) of the road.  Professionals who work on roads use the word "grade" to refer to the steepness of the slope of a road.

Professionals constructing roofs use the word "pitch" instead of "grade."  Clearly to understand grade, pitch, and their relationship to each other, one must have more than a simple understanding of the basic trigonometric function called "tangent" and the algebraic concept of "slope" that you've learned in previous classes.

The pitch of a roof is described the following way. If a plan calls for a 11/18 pitch roof, then the roof rises 11 inches for every 18 inches of horizontal.  (Horizontal is "run" in the image shown.)

Find the angle of elevation in the 11/18 pitch.  Then discuss the relationship between "pitch," "grade" of a road and "slope."  Furthermore, what does "tangent" have to do with "pitch," "grade" and "slope"?

Then find the full length of the total rise and the "rafter line" (refer to the illustration above) if the full length of the "run" of the rafter is 22 feet.  You'll need to think about similar triangles.

Your blog needs to (a) stand alone, that is, not require your reader to read JammnPeaches. (b) be written in complete sentences  (c) complete the math with explanations in English.

There's more cool math and geometry in these constructions, particularly when there's gables or two different pitches involved in a single house.  If you'd like to explore this OYO or in a blog post, feel free to do so. The reference below is excellent for this blog and for your future studies.  If you have Geometer's Sketchpad, then you can see the sketchpad illustration of the "valley" between two roofs of different pitches.

reference:
http://jwilson.coe.uga.edu/EMAT6680Su09/King/Roofing/Application%20of%20%20Mathematics%20in%20Construction.htm

Grade of a Road.

Driving East on I-70 into Denver, there's signs posted about the road being a "6% grade."  What's that mean?  Why is this posted on the highway?   A 9% grade is steeper.  Rock climbers think nothing of a 100% grade; many even climb an infinite grade.  mmm.  What's that mean? We've explored this briefly in class, in particular in regard to the Pike's Peak Cog Railway that sports a 25% grade in one section.

Do a short quick google search on "Grade of Road" or "Incline."

I've never seen or driven on an 18% grade or a 25% grade on a road; the 9% grade I drove on was steep enough.  What grades have you seen? I think there's a 12% grade into Jackson Hole, Wyoming.  Anyone drive on that grade?








Your blog: How is the grade of a road established? What's it mean to have an x% grade?  Explain.  Is this helpful information?

The grade of a road has EVERYTHING to do with the slope of a line.  What is the slope of a line?  How is this related?

Here's an image to help in your description:

In your blog, to earn full credit, you will need the following: (a) to connect trigonometry, slope, and grade together; (b) to include an application -- maybe something you saw on a road or read about.  You  may NOT write about the Manitou (Pike's Peak) Incline (that was already done in class); (c) to write complete ideas in full sentences. Your blog needs to stand alone -- that is, not require your reader to also read my blog. 

Images are great, but this is a blog with an implication that there's an essay there.  If you have any questions, please ask!