Why are baseball bases 90 feet apart?
For the same reason that home plate is shaped like a house. OK - seriously, here is a website to the origins of baseball that explains why 90 bases are 90 feet apart. "The basic layout of the diamond has been little changed since the original Knickerbocker Rules of the 1840s. The distance between bases was already established as 90 feet, which it remains to this day. Through trial and error, 90 feet had been settled upon as the optimal distance. 100 feet would have given too much advantage to the defense, and 80 feet too much to the offense. As athleticism has improved on both sides of the equation, 90 feet remains the appropriate balance between hitting and fielding, as it continues to provide frequent tests between the speed of a batter-runner and the throwing arm of a fielder." http://en.wikipedia.org/wiki/Baseball_fi...
Really hard math problem!?
a. The diamond is a square with each side = 90 ft, so using the Pythagoras formula the distance from 3rd base to 1st base = 90√2 = 127.28 ft b. This is a triangle with sides 45 and 90, and the hypotenuse is the distance to be thrown. Using the Pythagoras formula again, distance = √(90² + 45²) = √10125 = 100.62 ft c. Pitcher Mound to 2nd base = length of diagonal - 60 ft = 127.28 - 60 = 67.28 ft Pitcher Mound to 1st & 3rd are the same; using the law of cosines here, d² = 60² + 90² - 2(60)(90)cos 45 = 11700 - 7636.75 d² = 4063.25 d = 63.74 ft