Baseball...Law of Cosines

G

greatwhiteshark

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May 8, 2005
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The distance from home plate to dead center at Wrigley Field is 400 feet. How far is dead center from third base if each base is separated by 90 feet?
 
Janet, Janet, Janet!
What is there about this problem that you can't just write it out? You don't know what a baseball diamond looks like? You forgot the law of cosines? Did you draw a picture?
 
Gene

I found the distance from the pitching rubber to second to be 66.8 feet.
I then added 66.8 ft to 60.5 ft (the distance from the pitching rubber to home plate). I subtracted the sum from 400 feet and got 272.7 feet from second base to dead center. Knowing that each base is separated by 90 feet, I used the Pythagorean theorem and my answer is 287.2 feet from dead center to third base. However, the correct answer is
342.3 feet. How can this be?

Janet
 
Draw a diamond shape. Starting at home call it ABCD with D being third base. Each side is 90'. Draw a line from A thru C and extend it to E, 400' from home. The distance from D to line AE is 90/sqrt(2). Call it point F. That is also the length of AF. Add point G about 2/3 of the diamond side from A (a little farther than F) for the mound. Now you have the map.
Code: 
        E




        C

        G
   D    F    B


        A
I used the Pythagorean theorem and my answer is 287.2 feet from dead center to third base.
Click to expand...
Looks good that far, but it looks as though you used it on CE and CD. ECD isn't a right angle so it doesn't apply. You would have to use it on FE and FD.
Or you can find angle ECD and use the law of cosines with
ED² = CE²+CD² - 2*CE*CD*cos(ECD)
Same answer either way.

A good sketch always helps.
 
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