Use the image to answer the question. A shortstop is standing in the base path between second and third base when she fields the ball. She is 25 feet from second base and needs to make the throw to first base. Assuming the field is square, how far does she need to throw the ball? Round your answer to the nearest tenth. (1 point) feet Skip to navigation on the right it says 90ft

Answer 1

To determine the distance the shortstop needs to throw the ball to first base, we can visualize the baseball diamond as a square with each side measuring 90 feet. Since the shortstop is standing 25 feet from second base, this creates a right triangle where:

1. One leg of the triangle is the distance from the shortstop to second base (25 feet).
2. The other leg of the triangle is the distance from second base to first base (90 feet).

We can use the Pythagorean theorem to find the distance from the shortstop to first base. The theorem states that:

\[ c^2 = a^2 + b^2 \]

where:

• \( c \) is the hypotenuse (the distance the shortstop needs to throw),
• \( a \) is 25 feet (the distance from the shortstop to second base),
• \( b \) is 90 feet (the distance from second base to first base).

Plugging in these values, we get:

\[ c^2 = 25^2 + 90^2 \] \[ c^2 = 625 + 8100 \] \[ c^2 = 8725 \] \[ c = \sqrt{8725} \] \[ c \approx 93.4 , \text{feet} \]

Therefore, the shortstop needs to throw the ball approximately 93.4 feet to reach first base.