We’re laying the footings for an addition next week and it’s been a LONG time since highschool Trig.
The addition turns 22.5 degrees from the existing house and that’s throwing off my math skills. To make it simple lets say I have a triangle that is 10 ft on one leg and 28 feet on the other. The angle in between is 157.5. What is the long leg (hypotenus?) length.
I new I should have paid more attention in high school!
Thanks
Eric
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Replies
11.31'
11' 4"
Maybe I didn't explain properly but if the 2 short legs are 28 ft and 10 ft the long one must be longer than 11-4 or maybe that was a mistype! Thanks!
Eric
Edited 9/16/2008 2:22 pm ET by EricP
The Pythagorean Theorum - A squared plus B squared equals C squared.10 squared = 10028 squared = 784784 + 100 = 884The square root of 884 is 29.73214, or 29' 8 13/16".Just FYI - A right triangle with sides of 10' and 28' is at 19.7° - Not 22.5°
There is no right way to do something wrong.
http://www.trig.ionichost.com/trig.php?anglea=157.5&angleb=&anglec=&sidea=28&sideb=10&sidec=&submit=Solve+It!Looks like it is about 18.5'
You're getting all sorts of different answers, and I have no idea why. Everyone must be seeing this from a different perspective. Any chance you could post a sketch of what you're trying to do? then we'd all be trying to work the same problem...
A good carpenter doesn't blame his tools.
I most likely punched a wrong number in. I couldn't duplicate my answer. Anyways, I agree with the 29.732 number or 29' 8 12.57/16"
449.219 inches
using the law of cosines i also get 449.19 inches
We win. Split the beer?
37 ft 5 and 1/4 it is!!
That's a great trig website. I just added it to my favorites. Anyone know how to do this with a construction master calculator without relearning trig? I don't think mine even has trig functions.
Thanks to All!
Eric
Edited 9/16/2008 3:19 pm ET by EricP
You don't have to re-learn trig. Been surveying thirty years and have taught dozens of people short-cuts in trig that take all the mystery out of it.
You just reduce every problem to RIGHT triangles. All triangles have a total of 180 degrees. You just extend one leg and make an obtuse or acute triangle a right triangle with an angle of 90 degrees, and calc the remaining angle. Then it's a simple matter to use sine/cosine/secant/cosecant/tan/cotan to calc the remaining legs.
Laminate a pic of a triangle and the functions and keep it with your calc. You'll be doin'em in your sleep...if yer really bored.
Just remember, it's not Rocket Surgery....
. . .just reduce every problem to RIGHT triangles.
. . . remember, it's not Rocket Surgery....
Somebody ought to tell that to the roof cutting wizards over at the "Rough Framing" forum part of the JLC site. Those professors of the frame can run a thread out to thirty or more posts on topics such as unequal pitch hips and heelstands.
But, hey, it's more entertaining than watching Judge Judy.
View Image
"A stripe is just as real as a dadgummed flower."
Gene Davis 1920-1985
I've seen lots of carps say, "I don't know trig."
Anybody that has used a framing square uses trig. It's nothing but rise & run. Once you reduce it to that level, everybody understands it....except roofers.
They're special. ;-)
Somebody ought to tell that to the roof cutting wizards over at the "Rough Framing" forum part of the JLC site. Those professors of the frame can run a thread out to thirty or more posts on topics such as unequal pitch hips and heelstands.
Then in swoops Gene with questions for the same framers http://forums.jlconline.com/forums/showthread.php?t=44440 about the math. Then when the thread stops after a few posts, well let's go to Breaktime and ask the same question http://forums.taunton.com/n/mb/message.asp?webtag=tp-breaktime&msg=109797.1&maxT=7
Why the continual disrespect Gene?
Where is the disrespect, Tim? I'm as longwinded as many here, and over at JLC as well.
Look at how long I can drag on over a kitchen layout.
But as for right triangles, those little three-sided guys don't have much to say. Sin, cosine, tangent, a few inverts, that's all.
View Image
"A stripe is just as real as a dadgummed flower."
Gene Davis 1920-1985
I didn't read anything sinister in your post either. Tim and you must have some history that I don't know about.
Ok, I misread you.
Thanks for the replies so far!
Let me explain again although I think JAlden may be right. It is not a right triangle but thanks Boss!
The addition comes out 10 ft and then turns 22.5 degrees from the existing foundation line. It then goes 28 ft. So I essentially have a triangle with one short leg 10 ft, the other short leg 28 ft and the angle in between 157.5 degrees. I'm looking for the lenght of this long leg. It will NOT be part of the building but only a reference to get the angle right for layout. Is there a simpler way to lay this out?
Eric
Looks like this?
I get ya now. It's actually 37' 5 1/4".Or another way of checking it - Run the strong line straight out, parallel with the 10' wall. At the point where the 28' wall ends it should be 10' 8 1/2" above the string line.
The ship of failure floats on a sea of excuses.
If you're looking to get an accurate angle you can use the following,
Circumference = pi times diameter
So what you ask?
Cir. divided by pi ( 3.14 ) = diameter
360" div. by 3.14 = 114.6"
Think of 360" as 360 degrees of a circle.
Half of the diameter gives you a radius of 57.3"
Swing an arc from the intersection of your two legs with a stick 57.3" long
Measure along the arc for 22.5" and that's precisely 22.5 degrees.
Measure 157.5" along the arc and you've got that angle.
Every inch of the circumference equals one degree.
The only thing you need to remember is 57 3/8"
With that you can layout any angle, for pretty much any thing...buic
Edited 9/17/2008 12:29 am ET by BUIC
Old books like "Railroad Curves and Earthwork," by Allen have literally hundreds of methods for laying out anything without an instrument. I can two-tape any curve once I know two elements of it.
Yeah, I'm a big believer in keep it as simple as possible.
Less chance to mess up! buic
Using the law of cosine I got 37.43 or 37'5".
I get 37'-5 1/4" along that dimension. Your large angle is 157-30, the angle from the 10' leg along the hypotenuse is 16 deg-38', and the angle from the 28' leg to the long dimension is 5 deg-52'.
Unless I'm seeing something wrong...
Looks like you already have your answer, the long leg of your triangle is 37.43491.
Calculators for the quick answers: Triangle Solvers
Use the Law of Cosines if you have a scientific calculator.
Make a rough sketch of your triangle, and label the angles A, B and C, and the sides opposite the angles a, b, and c.
Law of Cosines: a² = b² + c² – 2bc cos A ... where b and c are the short legs of your triangle and angle A is the included angle between them. Substituting your known values in the formula:
a² = 10² + 28² – 2 × 10 × 28 × cos 157.5°
a² = 100 + 784 – 560 × (–.92388) ... note the negative value for the cosine since the angle is greater than 90°; the two negative numbers combining to make the last term postive.
a² = 1401.37254
Taking the square root of both sides of the equation solves for side a = 37.43491
That's just the formula without the explaining reason why it works but you can probably Google up a hundred sites that will show the derivation of the formula with a drawing. Also, note that if the included angle = 90°, cos 90° = zero and the last term drops out of the right hand side of the equation, leaving us with:
a² = b² + c² ... the Pythagorean Theorem
Joe Bartok
Edited 9/16/2008 3:29 pm ET by JoeBartok
Edited 9/16/2008 9:45 pm ET by JoeBartok
Eric, here is a link to Law of Cosines, courtesy of Wikipedia.
If you scroll down the page to the section titled "Proofs" you'll find a proof of the Law of Cosines using the Pythagorean Theorem. I don't know a lot about Construction Master Calculators but I do know they handle right triangles easily enough, and someone adept at using a CM ought to be able to "translate" that proof for you.
Just a bit of advice: When faced with something like this I almost always do a scale drawing and compare whatever computed answer I get with the drawing. It's easy to slip a digit or get an angle backwards, but much harder to mess up the drawing.