To solve the problem, let's analyze the situation using the information given.
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Vertices:
- Assume the square baseball field has its bases positioned at the vertices. Let:
- A (1st Base) be at (0, 0)
- B (2nd Base) be at (90, 0)
- C (3rd Base) be at (90, 90)
- D (Home Plate) be at (0, 90)
- Assume the square baseball field has its bases positioned at the vertices. Let:
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Position of the Shortstop:
- The shortstop is in the base path between second base (B) and third base (C) and is 30 feet from second base.
- Therefore, her position can be calculated as:
- 30 feet towards third base means she is positioned at (90, 0) + (0, 30) = (90, 30).
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First Base Position:
- First base is at (0, 0) as assumed above.
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Calculating the distance:
- To find the distance from the shortstop’s position at (90, 30) to first base (0, 0), we use the distance formula:
where and .Plugging in the values, we get:
Approximating
: -
Rounding:
- Rounding to the nearest tenth, the distance the shortstop needs to throw the ball is approximately 94.9 feet.
Therefore, the final answer is: 94.9 feet.