a baseball diamond is a sqaure 90ft on a side. the pitching rubber is located 60.5 ft from the homeplate…?
… on the line joining home plate and second base. how far is it from the piching plate to the 1st base? to 2nd base? if a pitcher faces home plate, through wat degree angle does he have to turn to face first base?
the line drawn from homeplate to the pitching plate intersects a 90 degree angle, making a 45 degree angle, thus making a 45-90-45 triangle. does this mean that the disctance from the pitching plate to 1st and 2nd base is equal? i need a little explnation for that, im getting a bit confused. thnx!!!
The rubber (aka pitching plate) is not in the middle and that will be shown. Consider the lengths from home to 1st, 1st to 2nd, and 2nd to home. That is a 45-45-90 triangle so we can calculate the length from home to 2nd to be 9*sqrt(2) = 127.28 ft and the halfway point is 63.64 ft, clearly the rubber is short of the halfway point, and visually it is obvious.
So to find the distance from the rubber to 1st, we can calculate the length from the rubber to 1st since we know the angle formed by the lines of 2nd to home and home to 1st is a 45 degree angle. Thus we can assume that the lines from the rubber to home also forms a 45 degree angle. The best way to do it would the the law of cosines i think.
b^2 = a^2 + c^2 -2a*c*cos(B), where:
b is the length from the rubber to 1st
a is the length from the rubber to home
c is the length from home to 1st
B is the angle formed.
Using our information,
a = 60.5, c = 90, B = 45 degrees, we get
b^2 = (60.5)^2 + (90)^2 – 2*60.5*90*cos(45 deg)
= 4059.85 ft^2
and taking the positive square root we find that
b= 63.72 ft which is the length from the rubber to 1st.
To find the distance from the rubber to 2nd, simply
127.28 – 60.5 = 66.78 ft
To find the angle that the pitcher has to turn we can do the arctan to find it. So,
arctan(63.72/60.5) = arctan(1.05) = 46.48 degrees
The original design was meant to be 66 ft 6 in i believe but the person working on the mound confused the middle 6 for a zero and so that is why we 60.5 ft.
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