Dead Center
Dead Center
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The distance from home plate to dead center field is 401 feet. A baseball diamond is a square?
with the distance from home plate to first base is 90 feet. So how far is it from first base to dead center field
Break it down into right triangles. Divide the infield into 4 right triangles by establishing a line between home and 2nd, and between 1st and 3rd. Where they meet is the center of the infield (the diamond). Because you're bisecting the lines, the distance from the center to any base is the same.
The triangle formed by home, 1st and the center has the hypotenuse as the first base line, which is 90 feet. Pythagorean theorem: a^2 + b^2 = c^2. In this case, a = b, so it can be written 2a^2 = c^2. 2a^2 = 90 * 90 = 8100. a^2 = 4050. a = sqrt(4050), which is about 63.64 feet. That's the distance both from home to the center and from the center to 1st.
Another right triangle is formed by the line from 1st to the center of the diamond, from the center of the diamond to dead center field, and from 1st to dead center field (the hypotenuse). The distance from the center of the infield to dead center is 401 - 63.64, or 337.36 ft. Using Pythagoras again, (337.36)^2 + (63.64)^2 = x^2. 113811.77 + 4050.05 = 117861.82 = x^2. sqrt (117861.82) = sqrt(x^2) = x. 343.31 = x.
The distance from first base to dead center is approximately 343.31 feet