To determine how far the shortstop needs to throw the ball from her position between second and third base to first base, we can visualize the baseball field as a square. The distance between the bases is generally 90 feet.
Given:
- The shortstop is 35 feet from second base.
- This means she is \(90 - 35 = 55\) feet from third base.
We can place the bases in a coordinate system where:
- Second base is at \((90, 90)\),
- Third base is at \((0, 90)\),
- First base is at \((0, 0)\).
If the shortstop is positioned directly between second and third base, her coordinates could be represented as \((55, 90)\), indicating she is 55 feet from third base toward second base along the line between those two bases.
To find the distance from the shortstop's position to first base, we can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] where:
- \((x_1, y_1)\) are the coordinates of the shortstop \((55, 90)\),
- \((x_2, y_2)\) are the coordinates of first base \((0, 0)\).
Substituting in the coordinates: \[ d = \sqrt{(0 - 55)^2 + (0 - 90)^2} = \sqrt{(-55)^2 + (-90)^2} \] Calculating the squares: \[ = \sqrt{3025 + 8100} = \sqrt{11125} \] Now, we compute the square root: \[ d \approx 105.4 \]
Rounding to the nearest tenth, the shortstop needs to throw the ball approximately \(105.4\) feet. Thus, the final answer is: \[ \boxed{105.4} \]