A shortstop is standing in the base path between second and third base when she fields the ball. She is 30 feet from second base and needs to make the throw to first base. Assuming the field is square, she needs to throw the ball approximately [blank] ft.

Answer 1

To calculate the distance the shortstop needs to throw the ball from her position to first base, we first need to understand the layout of the baseball diamond.

1. Field Layout: The bases are arranged in a square, with each side measuring 90 feet. The positions of the bases are as follows:

   • Home Plate (HP)
   • First Base (1B)
   • Second Base (2B)
   • Third Base (3B)

2. Shortstop's Position: The shortstop is positioned between second and third base. She's 30 feet from second base.

3. Calculating the Distance to First Base:

   • From the shortstop's position to second base is 30 feet.
   • The distance from second base to first base is 90 feet (the length of one side of the square).
   • To find the total distance from the shortstop to first base, we can visualize the situation as a right triangle:
     • One leg of the triangle is 30 feet (distance from the shortstop to second base).
     • The other leg of the triangle is 90 feet (distance from second base to first base).

4. Using the Pythagorean Theorem:

   • The distance from the shortstop to first base (hypotenuse) can be calculated as follows: \[ d = \sqrt{(30^2) + (90^2)} = \sqrt{900 + 8100} = \sqrt{9000} = 30\sqrt{10} \]
   • Evaluating this gives approximately: \[ d \approx 30 \times 3.162 = 94.86 \text{ feet} \]

Therefore, the shortstop needs to throw the ball approximately 95 feet to first base.