Monday, It's a new week.

too much math

since i've been working with my daughter all weekend on her geometry homework I may have to get her to co-sign the answer to this question. When told, she said it was a gross question and I told her she's way overboard.

Going completely out on my own, I'd say your error is roughly your preferred accuracy in answering times the my wife's favorite amendment to the constitution. With all these women around, when do I get the vote!

spoiler at end, don't read anymore if you want to work out the numbers ;-)

Thanks for the brainteaser ...

law of cosines sqr(a) = sqr(b) + sqr(c) - (2bc)(cos(ang(a)))

Target for "perfect" is around 141 feet 5 and 9/16 inches.

If you "go wide" 141 feet 6 and 3/4 inches.

oops....posting removed space in answer

meant to have blank lines between rough numbers and math ... sorry if I spoiled it.

Re: Monday, It's a new week.

Randy was dead on. A star for your forehead. I especially liked the co-sign. The amendment reference stumps me still. I thought it might be 2-"Bare" Arms, or 22 (term limits), or 19 (no sex discrimination for voting) or even 21 (the repeal of prohibition sorry--joke). Anyway let me know which one was in your thinking. My answer is as follows.

Part B. I don�t remember if it was a Mad magazine t-shirt or Rocky and Bullwinkle who said it, but �Doesn�t anyone know the Pythagorean Theorem around here?

Here goes-- last part first. What we have here is an isosceles right triangle with two sides equal (100 feet) complete with the required a ninety degree corner. Now we all know that Pythagoras opined a2 + b2 =c2. Anyone remember that? Bueller, Bueller? OK. If that is correct then (100 x 100) + (100 x 100) =c2 (I couldn't get the notation to work but c2 is understood to be c squared and NOT part of the family of plastic explosives)

10000 + 10000 = c2

20000 = c2

square root of c2 is 141.421356 feet �but that is decimal feet

so 141 feet + .421356 works to 5 inches and the remainder is 9/16�.

Now to part A . Here�s where we all collectively say �Where does he get this, well...stuff�? Not as elegant as Randy. One way to think on this is to set a 100 foot string. If you start at the corner and go to precisely 90 degrees, then move the string seven minutes worth (not clock minutes but degree minutes--but I digress--how far will the end of the string move from being precisely �square� at 90 degrees? Forget that cal-cu-lus. I did it, with help, by mentally rotating the string one revolution or the full 360 degrees. That is the circumference of a circle and the formula is 2 times pi (3.14) times the radius of the circle which is, of course 100 feet. How much the end moves in inches is the problem. So, the equation is error over 2 times pi times the length is equal to the angle over 360 degrees. This is: error equals the angle times 2 times pi times length divided by 360.

This evolves to: error = angle times length times pi divided by 180. In degrees.

A minute is 1/60 of a degree and the error is seven minutes.

Error + (7/60) (100 feet) (3.14 divided by 180)

= 0.2036 feet

=0.2036 times 12 inches

=2.44 inches

2 7/16" + or � on either side of exact 90 degrees (which you can check using old Pythag.(I call him that cause he's one of my peeps)

The lesson here is to use a better transit. A possible 2" out in 100 feet is too much.

Re: Monday, It's a new week.

Gary,

My "error" was calculated for the diagonal, not the end point difference. So I was going for the 19th amendment, women's right to vote... although my wife if pushed would probably prefer to have her glass of wine with dinner than vote ;-)

Cos(90) = 0 so law of cosine resolves to pythagorian equation for right triangle, but comes in VERY handy when you've got no right angle to trust.

Thanks for the question!

Randy

Funny thing about that ;-)

Last year I was helping one of my daughters with a problem that ended up needing the law of cosines to solve. Unfortunately, I didn't remember it, but in the process of solving the problem a slightly different way, I ended up deriving the formula for it. It is fun when something like that happens.

Re: Monday, It's a new week.

If I understood your problem the diagonal measurement would be

141.42136 feet to be square.

Re: Monday, It's a new week.

sThe answer is off the chart. The square root of c2 is 141.421356 feet �but that is decimal feet

so 141 feet + .421356 works to 5 inches and the remainder is 9/16�.