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