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The last house I framed had two outside corners at 67.5 degrees. To snap out the foundation I used basic geometry. I know that 67.5 degrees is the level cut for a 5/12 pitch, with that in mind I snapped out a 5/12 for the 67.5 corner. It was a pain because the foundation walls were really tall and I had to set up square inside the hole to find the 67.5 degrees. I was wondering if anyone out there had the trig formula for finding the hypotunse of a obtuse triangle if you know to legs. Any info would be greatly appreciated!
Thanks for your time,
Jeremiah Mercier
Replies
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sohcahtoa
*Jeremiah,Suppose you know the lengths of 2 sides of a triangle, side a and side b, and the measurement of the angle that these two sides make with each other.Example: side a= 36", side b= 40", and the angle that they form = 135º.the third side, c, which lies opposite the known angle of the triangle, angle C, can be found using the "Law of Cosines", which isc² = a² + b² - 2(a)(b)Cos C, where C is the angle that the 2 known sides form.In this example, c² = 36² + 40² - 2(36)(40)Cos135ºc² = 1296 + 1600 - 2880Cos135ºc² = 2896 - 2880(-.7071)c² = 2896 + 2036.45c² = 4932.45Therefore, c = square root(4932.45)c = 70.23 or about 70 1/4"Let me know if this helps. Ken
*That only works on right triangles, doesn't it ?
*Boss: Ken has it right. If this were a right triangle, then the cosine of 90 degrees is 0, effectively reducing the formulae to the right triangle formulae of c2 = a2 + b2 If this right angle is increased and this angle approaches 180 degrees, the cosine of the angle approaches 1. Also, if this right angle is decreased and approaches 0 degrees, the cosine of the angle again approaches 1
*Hi Stan,That's correct. This formula works for any triangle. As you said, if the angle that the 2 sides form is 90º, then 2(a)(b)Cos90º = 0, since cos90º = 0.So the formula,c² = a²+ b²-2(a)(b)cosC, reduces toc² = a²+ b², the well known Pythagorean theorem.Stan, here's a little tip that you might want to know.If you want to type c², intead of c2, after you type the c, hold down the alt key and type the number 253 over on the right side keyboard. (don't use the numbers at the top of the keyboard)Also, if you want to type 90º, instead of 90 degrees, after you type the 90, hold down the alt key and type 167 on the right side number keyboard.Ken
*Ken: I dont have any numbers except the row on top of my letters. Thanks for trying to help. We went over this one other time, and I am still having to do it the clumsy way.
*Ken: The last time we went over this, you wanted to see a picture of my keyboard. I was not able to then , but here it is now.Please instruct on how to get degrees, square signs, etc. Thanks
*Stan,Forget what your keyboard looks like.Look for 'character map' on your computer. (Go to the start button, then programs, then accessories, etc...)Open the character map. Highlight the character you want.Choose copy.Right click in the edit box here, and choose paste.To make things a bit more simple for myself, I made a shortcut to the character map, in my start menu.
*Luka: Thanks so much for trying to help me. I have the IQ of an unborn rhinoceros when it comes to computers. I tried everything you told me, and my character map doensn't having any degree or square symbols in it.
*Ken,That makes sense althouth I was thinking if I didnt know a or b and only knew the angle of 67.5 I would be right back where I was.It would be more helpful if I could use different numbers for a or b to create a larger obtuse angle. The wall that was 67.5 was almost 30 feet long so I wouldnt feel comfortable using such small numbers to snap it out. Thank you for your time!Jeremiah
*jeremiah,I'm sure I could be of more help if I understood your specific situation better. I've read over your original post several times, but I'm still not really sure what the wall layout looks like.There are a variety of different ways that math can help you in these situations, but unless I understand the problem better, I can't really say what they are.Would you consider taking another stab at explaining the wall layout? Keep in mind that you can see it in your head, but I have only words to go on.Ken
*Ken,The outside corner is 67.5 degrees instead of a 90 degree corner.So what I am trying to figure out is the math for the longest side of the triangle only knowing the 67.5 degrees kinda like you do with a2+b2=c2. Hope that makes some sense. The formula you gave is pretty much it I just dont know a or b.
*you can solve for any part of a triangle if you know 2 of the parts.. either adjacent side (A) , opposite side (O), or hypotenuse (H).. or any included angle... diagram it.. if you have or need AH, use the Cosine..if you have or need OH, use the Sine..if you have or need OA.. use the Tangent...you can also solve for the included angle with these same functions..most of these functions are found on any common scientific calculator...the acronym for remembering the relationships is the old indian name SOHCAHTOA...they can also be solved with log tables.. or slide rules.. but it would take me a week to remember how...
*Please excuse me for interrupting Ken. Jeremiah you don't have enough information to calculate side "c" with just the angle and no other sides given. If you want to understand it better, get a protractor and draw your 67.5º angle, as the sides adjacent to the angle change length the side across from the angle changes length. You need side "a" or "b" or another angle measurement to define your triangle. Can you supply another angle measurement and one sides length?Terry
*JeremiahThere is not enough information in your drawing to solve for the side opposite the given angle.Based on rereading your original post I get the impression that all you are after is a way to lay out a large 67.5º angle. If this is true then do the same thing you would to lay out a large 90º angle. Make a 3-4-5 triagle, only multiply the 3-4-5 by a common multiplier say 7 and make it a 21-28-35 triangle. Use the formula Ken gave you. Assign any values you want for sides 'a' and 'b' and solve for 'c'. If you want a larger triangle multiply all of the sides by the same multiplier.I hope this helps, if not please give us a value for the undetermined side in your drawing.Terry
*Test. If the symbols show up here for you, then do this...Create a new text file on your desktop or in your start menu. Open that text file. Copy the symbols from here, and paste them in that text file. Then any time you want to use them, open that text file, and copy them and paste them where you want to use them.Degrees... °Squared... ²Also, check out what font is being used when you open the character map. It shows in the upper left hand corner. Change that to arial, and you should see the symbols you want. I believe my character map came default with 'symbol' font selected for the character map. It seems that arial is the most common font out there, so whatever symbol you copy out of the character map using arial as the font for the CM, should mean that your symbol should show up here and on anyone else's computer.
*Not enough information, indeed. This is what I get on my screen...b : )
*Terry, Your right about not enough info. I went out to the garage with my calculator and a piece of plywood and Kens equation. I did what you said and assigned any two values for sides a and b. After crunching the numbers and swinging a couple of arcs with my tape I came up with 67.5 degree angle. Thank you so very much for your help and patience.
*jeremiah,Terry's assessment of your problem is correct. You just don't have enough information in your drawing to determine the side you have marked "want to find".What information do we have?We know that one side = 12', and the obtuse angle equals 180º - 67 1/2º = 112 1/2º.Now, if you knew how long the side which you have marked "undetermined" was, you could find an answer.Or, if you knew how many degrees there were in one of the other angles, you could find an answer.But as you show it, the side you "want to find" depends on how long the "undetermined" side is. As the undetermined side gets larger, the side you want to find gets larger. In other words, there are infinitely many possible solutions to the problem as you show it.Does that make sense?Jeremiah, I just posted this and saw that you had just posted a reply to Terry while I was typing this, but I'll leave it posted anyway.Ken
*Ken,Thanks for your help, it makes perfect sense now. I was for some reason trying to figure it out without knowing a and b.Jeremiah