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The Official Baseball Rules describe how to lay out a baseball diamond as follows:
Rule 2
The Playing Field
2.01 Layout of the Field
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When location of home base is determined, with a steel tape measure 127 feet, 3 3/8 inches [*] in desired direction to establish second base.
From home base, measure 90 feet toward first base; from second base, measure 90 feet toward first base; the intersection of these lines [!] establishes first base.
From home base, measure 90 feet toward third base; from second base, measure 90 feet toward third base; the intersection of these lines [!] establishes third base.
The distance between first base and third base is 127 feet, 3 3/8 inches.
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[This is not a true geometric construction, because a tape measure is used, but it is a way to create (nearly) right angles at first and third bases.]
[*] 90*sqrt(2) feet = 127.27922... feet
127 feet 3 3/8 inches = 127.28125 feet, an error of ~0.02 inches.
[!] Arcs of circles!
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