a major league baseball "diamond" is actually a square,90 feet on a side.what is the distance directly from home plate to second base(the diagonal of the square)?
2006-09-03 13:14:32 · 7 answers · asked by daranguyen_kpop4ever 1 in Science & Mathematics ➔ Mathematics
Think about the problem this way...the baseball diamond is a square. Taking the diagonal will leave two right triangles, with 90 ft on each side.
Using Pythagoras Theorem,
Diagonal d= sqrt(A^2+B^2)...in this case, A = B = 90 ft
or d = sqrt(2)*sqrt(90^2) = 127.28 ft
2006-09-03 13:25:11 · answer #1 · answered by alrivera_1 4 · 0⤊ 0⤋
Suppose there are two runners on base. Then the batter and the two runners are on the vertices of an isoceles right triangle, if the baseball diamond is built according to baseball rules. The distance from the batter to the first base runner is 1 base-to-base(b2b) length(provided the runner has not taken a lead - pitcher should try picking him off if he does). The distance from the first base runner to the second base runner is also 1 b2b. Since this is a right triangle, the Phythagorean theorem holds, so that
D^2 = 1^2 + 1^2,
where D is the desired distance. This means that D^2 = 2, so that D = sqrt(2) b2bs. Since a b2b is 90 feet, the distance is 90*sqrt(2) or about 127 feet.
2006-09-03 17:00:19 · answer #2 · answered by alnitaka 4 · 0⤊ 0⤋
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2016-10-01 06:49:41 · answer #3 · answered by kampfer 3 · 0⤊ 0⤋
Since the diamond is a square, there must be a right angle at first base. If you go directly from home plate to second base, that makes a triangle with the 'home to first base' side and the 'first to second base ' side.
Use the Pythagorean Theorem to solve.
2006-09-03 13:19:36 · answer #4 · answered by Bob G 6 · 0⤊ 0⤋
Using pythagoras
a^2 + b^2 = c^2
8100 + 8100 = 16200
So ur answer is the square root of 16200 whatever that is...
2006-09-03 13:21:16 · answer #5 · answered by Anonymous · 0⤊ 0⤋
90 feet?
2006-09-03 13:20:04 · answer #6 · answered by deepbushhunter69 3 · 0⤊ 0⤋
127'3.35"
2006-09-03 16:01:15 · answer #7 · answered by Jason J 2 · 0⤊ 0⤋