To determine how far the shortstop needs to throw the ball from her position on the field (30 feet from second base) to first base, we can visualize the baseball diamond as a square.
Let’s denote the bases as follows:
- Second base (B2) is the point where the shortstop is standing, which is 30 feet from second base.
- First base (B1), second base (B2), third base (B3), and home plate (H) form a square with sides of equal length.
In a standard baseball diamond:
- The distance between each base is 90 feet.
- The shortstop is standing 30 feet away from second base (B2).
Now, to find the distance from the shortstop to first base (B1), we can visualize the problem using the coordinates of the bases:
- Second base (B2) can be considered at the origin (0, 0) of a Cartesian coordinate system.
- First base (B1) is located at (90, 0).
Since the shortstop is standing 30 feet from second base, we find her position. Being on the base path and moving towards third base (B3) means the shortstop is positioned at (-30, 0).
Now we can calculate the distance from the shortstop's position (-30, 0) to first base (90, 0):
Using the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\): \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Plugging in the coordinates:
- For the shortstop: \((-30, 0)\),
- For first base: \((90, 0)\):
\[ d = \sqrt{(90 - (-30))^2 + (0 - 0)^2} \] \[ d = \sqrt{(90 + 30)^2} \] \[ d = \sqrt{120^2} \] \[ d = 120 \]
Thus, the shortstop needs to throw the ball 120 feet to reach first base.
Finally, rounding to the nearest tenth, the answer remains:
\[ \boxed{120.0 \text{ feet}} \]