OT- trigonometry problem

Mike (WA) · Nov 23, 2009

Son and wife asked for a combination firehouse/ dollhouse for grandson and granddaughter. Making it a combination seemed like a disaster in the making, so told them I wouldn't do a combination, but would sure do one for each. Son came over to work with me (never did much of that as a child, too interested in books- but now wishes he had more practical knowledge).

Got to the roof- gonna be a 4/12, and we were trying to figure out what the mitre should be. From somewhere in my troubled past (I helped my dad the carpenter a lot as a kid), about 17 1/2 degrees kept coming up in my head. Son is trying to solve it with trig- but he's 15 years out of high school, and is a newspaper editor, so is a little rusty with the math. I ended up drawing and cutting out a triangle on heavy paper, stood it up next to the radial arm saw blade and adjusted it accordingly (came out just about 17 1/2 degrees, and worked perfectly, by the way).

My question is- without resort to any trig tables or super whiz-bang calculators that we didn't have, could we have come up with the angle using trig?

Bob M · Nov 23, 2009

Mike - You need a calculator or trig table to figure that out.

For a 4/12, divide 4 into 12, then take the inverse tangent of the result. (The angle incidentally calculates 18.4 deg)

Don't have a calculator or table? There's one built in to Windows:

Click on "Start" then "all programs". From the list now select "accessories > calculator".

When the calculator appears on the screen click "view" and select "scientific" to get the calculator with trig functions.

JMOR · Nov 23, 2009

Without tangent tables or a calculator capable of inverse tangent, I don't think you could. There are framing squares marked for rise over run angles that would get you there.

Slope= tangent (rise/run)=tangent (4/12)= 0.333

angle=inverse tangent= inv tan(0.33)=18.4 degrees

a reasonable approximation is obtained by:

r X angle = arc length X 57.3

angle = (arc length X 57.3) /r

angle = (4 X 57.3)/12 = 19 degrees

ChrisLSD · Nov 23, 2009

for any calculator with the trig keys -
inverse sin(4/12) = 19.4712 degrees

i can only get google to do the sine and then it wants everything in radians so I gave up
but as a check enter this in a google search box

sin(19.4712*pi/180)

and hit enter - it gives the answer of .3333 approx which is what 4/12 is......

ChrisLSD · Nov 23, 2009

yup, inverse tangent was right - what i was thinking = 18.4349

or in google tan (18.4349/180*pi)

ScottyHOMeY · Nov 23, 2009

Using trig without a calculator programmed for it, you'd have had to go to tables at some point.

The angle of the rise above a horizontal length would be a tangent function. The ratio of the rise to the horizontal travel (4/12) gives you the tangent (0.3333) which is the number you'd then take to look up in the tangent tables. In this case your eyeball of 17-1/2 is close. Depending how fine your tables run, you would find it to be >18 and <19. A little hand interpolation would get you there, but the calculator puts it at 18.435*.

Mike (WA) · Nov 23, 2009

Interesting that you brought up the framing square- as I was typing this in this AM, I thought about that too- but I think my dad's old square that I inherited is long since illegible.

Thanks, guys- I think son was at the point where he may have gotten it with tables, but gave up because he didn't have them.

Coloken · Nov 23, 2009

Easy direct read of of a slide rule..except I can't read the little numbers any more.

spacechem · Nov 23, 2009

Well I'm considerably more than 15 years out of highschool, but I've managed to remember a trick we learned. It's a mnemonic- SOH CAH TOA. In those pre-PC (by that I mean politically correct) days, we pretended they were words in an indian language.

SOH stands for Sine = Opposite over Hypotenuse.
CAH is for Cosine = Adjacent over Hypotenuse.
TOA stands for Tangent = Opposite over Adjacent.

Depending on which two of the three lengths you happen to have- in this case you have the Opposite (4) and the Adjacent (12)- you divide the 4 by the 12 and take the result to your handy Tangent Table (we have ours hanging over the mantle) to get the angle you need, which is what other posters have already done...

Rob in Ore · Nov 23, 2009

I don't have any trig knowledge for you but many times I've used a T-bevel to get an angle, then taken that to my miter saw to read it. Of course, the framing square is WAY easier for the roofing projects.

T_Bone · Nov 23, 2009

Hi Mike,

You could have liad it out quicker than asking the question.

Right tri-angle drawn 4" vertical and 12" horizontal, measure the angle.

T_Bone

JMOR · Nov 23, 2009

kito169 · Nov 23, 2009

If your talking common rafters (single miter) it is just 4/12( 4" rise in 12" horizontal run). Where the 17 comes in is on hip and valley rafters (compound miter). Just go to some hardware store and buy a cheap plastic speed square and lay off the 4/12 then it will give you the angle. Rick

kito169 · Nov 23, 2009

JMOR's picture is perfect.

barn E · Nov 23, 2009

I can remember trig. All Sailors take chances. Don't know what all is. Sailors is sine, take is tangent and chances is cosine. A=Oscar harvey=O over H. (opposite and hypotenuse) S=ate heap=Adjacent over hypotenuse. T=opposite over adjacent C= Anybody remember EXACTLY how this goes. Also used in Navy and Marine core. Dave

JMOR · Nov 23, 2009

(quoted from post at 23:05:11 11/23/09) I can remember trig. All Sailors take chances. Don't know what all is. Sailors is sine, take is tangent and chances is cosine. A=Oscar harvey=O over H. (opposite and hypotenuse) S=ate heap=Adjacent over hypotenuse. T=opposite over adjacent C= Anybody remember EXACTLY how this goes. Also used in Navy and Marine core. Dave

ounds like a drunk sailor to me???

NW Ohio Tim · Nov 24, 2009

Just use a framing square. on the endge of whatever your cutting,put the inside tail of the square on the 12 and the inside tongue of the square or 4. (Or use the outside numbers, just be consistant.) The The angle of the tongue is the angle you'll cut the top of the rafter. The angle of the tail is the roof slope and also the angle you'd cut the birds mouth at the bottom of the rafter.

It's easier to do than typwe. I'll take a picture later if that doesn't make sense. After you do this, you can use a t-bevel to lock the angle and do whatever you want.

Tim K in NW Ohio ~ Who's Grandpa coulf draw a circle with a framing square.... wish he was still around.

OT- trigonometry problem

Mike (WA)

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Bob M

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JMOR

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ChrisLSD

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ChrisLSD

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ScottyHOMeY

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Mike (WA)

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Coloken

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spacechem

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Rob in Ore

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T_Bone

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JMOR

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kito169

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barn E

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JMOR

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NW Ohio Tim

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