Do we have a math guy in our mists?

[DalesCarpentry]

Do we have a math guy in our mists? I have been a carpenter for 23 years now and am good with math. Math has always been my thing and enjoy problem solving. I have had this question bottled up in me for 20 years and don't know the answer. I cut a lot of roofs and a 12 in 12 roof equals a 90 degree angle. To cut this roof you would cut the rafters on a 45 degree angle. Half of 90 degrees. It would stand to reason then that a 6 in 12 pitch roof would be 22.5 degrees. Half of a 12 in 12 roof pitch. That is not the case though a 5 in 12 pitch roof is 22.5 degrees. WHY!!!!!!!!!!!!! Do any of you have the answer. Dale

[mrloring]

It actually comes out to 22.62 degrees, but who is counting.

[mrloring]

The trigonometry formulas are

Sin(q) = Opposite / Hypotenuse
Cos(q) = Adjacent / Hypotenuse
Tan(q) = Opposite / Adjacent



opposite=5
adjacent=12

So we use the formula

Tan(q) = Opposite / Adjacent

And solve it this way

Tan(q) =5/12


(q) = 5/12
             Tan

(q) =22.61986495

[DalesCarpentry]

Ok then so if a 12 in 12 roof equals 90 degrees why does a 6 in 12 equal 26.56505 and not 22.5? Dale

[magooch]

You're trying to mix apples and oranges.  Just because the hypotenuse of a 12" run and a 12" rise happens to equal a 45 degree angle, it doesn't correlate that cutting the rise in half will cut the angle an equal amount.

[beemanbeme]

I'm not a carpenter but my Dad, who was, showed me how to use a framing square and I've never wondered about the degree of the angles.  They are what they are.  I have found being too smart can be a handicap and I am certainly not handicapped.

[DalesCarpentry]

I certainly know how to use a framing square. Dale

[crustaceous]

You're applying linear logic to a nonlinear function.  Imagine a clock with only one hand, the hand is the hypotenuse of the triangle and it's length never changes.  As the hand rotates the rise and run (opposite and adjacent sides) dimensions change. The hand is moving in a circular fashion (non linear) so that the relationship between the rise and run is changing in a nonlinear fashion as well. The relationship between the rise and run (opposite and adjacent)is the basis for sine, cosine, tangent etc. (trigonometry). Here's a site that to check out
http://www.cut-the-knot.org/Curriculum/Calculus/SineCosine.shtml

[DalesCarpentry]

Thanks. I think I finaly understand it now. Dale

[beemanbeme]

I didn't mean to imply that you didn't.  I  just never thought about the angles. 

[PHATINJUN]

Dale you got to learn to let that crap go to keep that bottled up inside your mind for 20yrs' must of been maddening Kurt

[DalesCarpentry]

Dale you got to learn to let that crap go to keep that bottled up inside your mind for 20yrs' must of been maddening Kurt

Yes it has been. I am good with math and can cut the most complex roofs there are without a problem. This is something that has bothered me for a very long time. I am happy I got the answer I needed.

I didn't mean to imply that you didn't.  I  just never thought about the angles. 

No problem I am sure you did not mean I did not know how to use one. Thanks all Dale