Re: Calculating slope of roof: What is the arc-sine of (4/12) ?!
- From: Jeremy Boden <jeremy@xxxxxxxxxxxxxxxxxx>
- Date: Sat, 21 May 2005 22:27:40 +0100
In message <428F9DE9.35F95BAD@xxxxxxx>, Math Guy <Math@xxxxxxx> writes
I have a "4-12" roof.
For every 12 inches horizontally it slopes 4 inches.
If you drew a right-triangle with 12 across the base (adj) and 4 on the side (opp), then
sin(theta) = opp / adj = 4/12 = .33333333
Working in radians - unless I'm mistaken, sin(0.3398369) = .3333333244
If I convert 0.3398369 into degrees (by multiplying it by (180/pi) I get 19.47122009.
On my scientific calculator, the arc-sine of (4/12) is 19.47122063.
HOWEVER
In my drawing program (coreldraw) If I rotate a horizontal line to match the slope of a rectangle (length 12, height 4 units) Corel tells me that the angle is 18.44 degrees.
Similarly, many websites show that the slope of a 4-12 pitch roof is 18 degrees (rounding to the closest degree I guess).
http://www.uspconnectors.com/referencematerial.shtml
This page:
http://www.dennisdavey.com/building%20jargon.htm
(around the middle of the page) says that a 4-12 pitch roof has an angle of "18 deg 28 min" (which is around 18.5 degrees - yes?).
So why am I seeing 2 different angular degree readings for this geometric shape?
Which one is right?
19.47 or 18.44?
If you have a roof which has a vertical rise of 4" for every 12" of horizontal distance then you want arctan(4/12) = 18.43 degrees.
(opposite/adjacent and all that...).
-- Jeremy Boden .
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