Question

The area of a baseball field bounded by home plate, first base, second base, and third base is a square. If a player at first base throws the ball to a player at third base, what is the distance the player has to throw?

Answer 1

To find the throwing distance between first base and third base on a square baseball diamond, you use the Pythagorean theorem resulting in a diagonal measurement of approximately 127.28 feet.

Step-by-step explanation:

The question asks what the distance a player has to throw the ball from first base to third base in a baseball field, which is shaped as a square.

We can solve this by realizing that the path from first to third base is the diagonal of the square. The length of one side of the baseball diamond is 90 feet (which is the distance between any two bases).

To find the diagonal, we use the Pythagorean theorem (a2 + b2 = c2), where 'a' and 'b' are the sides of the square and 'c' is the diagonal.

As both sides are equal, the formula simplifies to 2*(a2) = c2.

Substituting 90 feet for 'a' gives us 2*(90 ft)2 = c2, which calculates to 127.28 feet (rounded to two decimal places).

Answer 2

well the question doesnt show any number for a side or anything but we can solve this with algebra if we say that a side from one base to next has a length of x. so we know each side has length x and that the shape they make is square. This means we are only searching for the diagonal of a square.

remember that a diagonal forms and isoscoles right triangle with the 2 sides being equal and the diagonal as the hypotenuse. Using the pythagoream theorem we can say that
a^2 + b^2 = c^2

we said all side lengths are x so we can put x in for a and b and get

x^2 + x^2 = c^2

2x^2 = c^2

c = x * squareroot(2)

that is the basic fundamental answer that will always work when working with diagonals of squares.

so if the length between bases is 90 ft, we could plug this in and get
c = 90 ft * squareroot(2)
c = 127.28 ft