Wow, I am blown away by the math skills in this group. Marv Klotz's
solution is so far beyond my humble math ability that I am embarassed
to post the way that I solved the darn thing.

OTOH I got the same answer as the math whizzes so perhaps I am not so
dumb after all.

The author of the book gives the answer as 9.6771 feet. I got
9.677002 so I fugure that is probably close enough for government
work. Plus there has been so much rain around here lately I think
that my ladder sunk into the ground a bit more than his did.

I have posted my answer in the http://metalworking.com/DropBox/

The Excel file has not shown up yet so I have also posted the files at

http://neme-s.org/images/ladder.htm

My deepest respect to all you math whizzes who obviously paid more
attention in high school or college algebra than I did.

Errol Groff

Instructor, Machine Tool Department

H.H. Ellis Technical High School
643 Upper Maple Street
Dantieson, CT 06239

New England Model Engineering Society
www.neme-s.org

Errol, thanks for posting this. I used to be a bit of a math whiz but that
was years ago and although I did a lot of math-type thinking during my 20
year electronic engineering career, I didn't get to do much actual math. I
really find that I enjoy it. I wish more problems like this showed up. Some
time ago I posted a shop math problem I encountered, which I found to be
fun and challenging. For example, I showed it to my dad's old manager from
Boeing, who once got a PhD from MIT in mathematics, and he couldn't solve it.
Admittedly, he's been retired a long time now. Lots of guys on this NG solved
it within an hour of its being posted. That one is still available at:
http://www.tinyisland.com/shopmathprob1.pdf

if you want to go see it.

Grant Erwin

On Mon, 30 May 2005 01:33:27 GMT, Errol Groff
wrote:


Wow, I am blown away by the math skills in this group. Marv Klotz's
solution is so far beyond my humble math ability that I am embarassed
to post the way that I solved the darn thing.

OTOH I got the same answer as the math whizzes so perhaps I am not so
dumb after all.

The author of the book gives the answer as 9.6771 feet. I got
9.677002 so I fugure that is probably close enough for government
work. Plus there has been so much rain around here lately I think
that my ladder sunk into the ground a bit more than his did.

I have posted my answer in the http://metalworking.com/DropBox/

The Excel file has not shown up yet so I have also posted the files at

http://neme-s.org/images/ladder.htm

My deepest respect to all you math whizzes who obviously paid more
attention in high school or college algebra than I did.

Errol, you can do that in one line of your spreadsheet by letting
Excel's solver do the guessing. ( I tried it to make sure.) Add
a cell, let's say N4, that is the difference between the two angles,
which would be H4 - I4 in your sheet. Then have Solver adjust cell
A4 (wall height) until the number in N4 is 0. Powie, wall height =
116.124028 when Solver accepted a difference between the angles of
-1.11905E-07 (about 0.1 micro degrees) as "close enough". I started
with an initial value in A4 of 119.9. It helps to add a constraint
that B4 must be = 119.9 so Solver doesn't go off into the weeds and
fail by trying values of 120 or greater in A4.

Tools, Solver. If you don't see Solver you may have to add it as an
add-in: Tools, Add-ins, Solver Add-in. Solver does the trials
a whole bunch faster than you can and you need type in only one row.

This approach sure beats the hell out of algebra for speed. BTW, I
think everyone else who solved it used numerical methods too, so we
were just as "brute force".

Computers are shop tools every bit as much as calculators and
micrometers. It's silly to spend an hour or more solving a problem
with algebra that a 'puter can solve to acceptable accuracy in less
than a second after just a bit of typing.

Don Foreman wrote:

Computers are shop tools every bit as much as calculators and
micrometers. It's silly to spend an hour or more solving a problem
with algebra that a 'puter can solve to acceptable accuracy in less
than a second after just a bit of typing.


Speaking of acceptable accuracy, when you're talking about a ladder on
a wall 3" down from the 120" mark would almost certainly be close enough :-)

GWE