Baseball Square

Question

The bases on a baseball field form a square with sides measuring 90 ft long. The pitcher’s mound is equidistant from first base and third base, and is 60.5 ft from home plate. How much closer is the pitcher’s mound to first base than it is to second base, rounded to the nearest hundredth of a foot?

Answer 1

the diagonal of the square from home to 2nd is 90sqr2 = about 90(1.414) = 127.28 feet

distance from home to the pitcher's mound is 60.5 feet

the mound to 2nd base = 127.28 - 60.5 = 66.78

half of 127.28 = 63.64

63.64 - 60.5 = 3.14

construct a right triangle with hypotenuse squared = 63.64^2 + 3.14^2

that hypotenuse is the distance from the pitcher's mound to 1st base

distance from the mount to 2nd base = 67.28

hypotenuse = square root of (4050.05 + 9.86) = 63.72

66.78 - 63.72 = 3.06 feet closer to 1st base than to 2nd base