A baseball infield is a square. Each side measuring 90 feet. To the nearest foot, what is the distance from home plate to second base?
2007-04-12 05:34:41 · 3 answers · asked by LALALAND 1 in Science & Mathematics ➔ Mathematics
90 times sq. root of 2
2007-04-12 05:39:15 · answer #1 · answered by Scott H 3 · 0⤊ 0⤋
The distance between home plate and second base is the diagonal of the square, which has length equal to sqrt(2) times the length of a side. So the distance is 90*sqrt(2). The question requests an answer to the nearest foot, so you should use a calculator to multiply this out and round.
The mathematical reason for this is related to the Pythagorean theorem. The diagonal constructs a right triangle with legs equal to the side of the square. If the side of the square has length s, the length of the diagonal d satisfies the condition d^2 = s^2 + s^2 ==> d = sqrt(2*s^2) = s*sqrt(2).
2007-04-12 12:37:44 · answer #2 · answered by DavidK93 7 · 0⤊ 0⤋
from the wonderful pythagorean theorem (a^2 + b^2 = c^2 for a right triangle) we get immediately distance: d=90*sqrt(2)
2007-04-12 12:43:14 · answer #3 · answered by james 1 · 0⤊ 0⤋