besbol pizza slice question
In previous post, we mentioned the distance that President George W. Bush Jr. threw a besbol yesterday from the Pitcher's Mound at RFK Stadium in Washington DC to Home Plate: 60 feet 6 inches.
A baseball diamond is 90 feet on each side. In other words, the distance from 1st Base to 2nd base, or from 2nd Base to 3rd Base, or from 3rd Base to Home Plate, is 90 feet.
(Don't let that word "diamond" scare you -- it's just a square, with right angles.)
Because of that screwy printer's error in the 19th century, the pitcher's mound is NOT in the exact center of the baseball diamond. It's a little closer to Home Plate than the center of the diamond.
The Pitcher very frequently has to throw the besbol to the First Baseman.
What is the Exact Distance from the Pitcher's Mound to First Base?
Vleeptron needs the answer Ancient Greek style: All in Whole Numbers. You can use addition, subtraction, multiplication, division, and maybe a Square Root.
In other words, NOT in a decimal fraction which maybe never ends, like
57.2330183823663 ... (<-- wrong)
My brother cannot win the Pizza Slice because he asked me this question and I answered it last year.
posted by Vleeptron Dude | 16:27
9 Comments:
It's almost 64 feet. Just a tad shy. I can give you a decimal number if you want, but you already said not to. 63 feet 9 inches?
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Okay, the pizza-winning answer has to be in a FORM like this:
37 + SQR(53)
----------------
19
In other words, all the numbers have to be Whole Numbers, related to each other using only the operations
+ - x / and SQR (square root).
Such an expression will be the EXACT distance ... not an approximation.
62 ft 9 inches would be an acceptable FORM ... because it could also be
62 9/12 = 62 3/4 = 251/4 feet
but that's not the answer.
Is the A squared + B sguared = C squared equation only valid on Right Triangles?
If not, then the answer is 60.5 squared + Our Answer = 90 squared.
So it's the square root of 4339.75
....65'10'' seems about right.
OR my equation is only for Right Triangles and I'm stumped.
Another Very Important Calculation applicable here is that if whether I score this pizza slice or not, I'm pretty sure I've got at least a couple days worth of meals at that short list of Northampton dives you've offered up as prizes for past years of trivial pursuit success by us.
If I can just square away (pun!) a couple more meals, I can visit you and Mrs Elmer for a weekend and eat for free the whole way!
Oops, shoulda read 4439.75 which has a SR of about 66feet7inches
Simply coincidence BTW, that this late insight came to me at the posted time stamp.
the answer is 63.717 feet blah blah blah, but to put it into whole numbers is driving me mad...
this is a simple problem that was assigned in 8th grade. basic cosine law.
a^2 = b^2 + c^2 - 2*b*c*COS(A)
using this, the given information about the baseball diamond, and your own brain you end up with
a^2 = (60'6")^2 + 90^2 - 2*(60'6")*90*COS(45)
which eqauls ~ 4059.857153
take the square root of that, and you get 63.71700835... blah blah blah
so i guess if this counts, then this is the answer:
a = SQR( (60'6")^2 + 90^2 - 2*(60'6")*90*COS(45) ) feet
Chris ... uhhh ... no, you can't use Cosines. And your guiding method shouldn't be the Cosine Law, but rather the Pythagorean right triangle relationship.
You only can use
* whole numbers
* addition
* subtraction
* multiplication
* division
* square root
btw, Vleeptron is sorta closed now, and all the new action is at
http://VleeptronZ.blogspot.com
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