SOLUTION: A pee wee baseball diamond is a square, each side being 60 ft. long. The pitchers mound is 40 ft. from home plate. How far is the pitchers mound to first base?

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Question 956128: A pee wee baseball diamond is a square, each side being 60 ft. long. The pitchers mound is 40 ft. from home plate. How far is the pitchers mound to first base?
Answer by stanbon(75887) (Show Source):
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A pee wee baseball diamond is a square, each side being 60 ft. long. The pitchers mound is 40 ft. from home plate. How far is the pitchers mound to first base?
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Draw the picture.
Sketch a line from pitcher's mound to 1st base; Label it "a".
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The angle at home plate is 45 degrees. ; Label it "A".
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Let the side from home to pitcher's mound be "p"
Let the side from home to 1st base be "b"
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Use the Law of Cosines to get:
a^2 = b^2 + p^2 - 2*b*p*Cos(A)
a^2 = 60^2 + 40^2 - 2*60*40*(sqrt(2))/2
a^2 = 3600 + 1600 - 2400sqrt(2)
a^2 = 5200 - 2400sqrt(2)
a^2 = 1805.89
a = 42.5 ft
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Cheers,
Stan H.
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