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.

Question

50

9000

94.9

Answer 1

To determine the distance from the shortstop to first base, we can visualize the baseball field as a square. The distance between each base is 90 feet.

1. The shortstop is located 30 feet from second base.
2. The distance from second base to first base is 90 feet.

Now, we can find the distance from the shortstop to first base using the Pythagorean theorem. The layout forms a right triangle:

• The horizontal leg of the triangle is the distance from the shortstop to second base, which is the length of one leg (30 feet).
• The vertical leg of the triangle is the total distance from second base to first base (90 feet).

Using the Pythagorean theorem:

\( d^2 = a^2 + b^2 \)

Where:

• \( d \) is the distance to first base,
• \( a \) is the distance from the shortstop to second base (30 feet),
• \( b \) is the distance from second base to first base (90 feet).

Calculating:

\( d^2 = 30^2 + 90^2 \)

\( d^2 = 900 + 8100 \)

\( d^2 = 9000 \)

\( d = \sqrt{9000} \)

Calculating \( \sqrt{9000} \):

\( d \approx 94.87 \) feet.

Therefore, the distance from the shortstop to first base is approximately 94.9 feet.

So, the answer is:

94.9