To find out how far the shortstop needs to throw the ball to first base, we can visualize the transition from her position between second base and third base.
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Understand the positions: In a baseball field, bases are arranged as a square with each side measuring 90 feet. Therefore, the distance from:
- Second base to third base (along the baseline) is 90 feet.
- Second base to first base (across the diamond) can be calculated using the Pythagorean theorem, as these two bases form a right triangle.
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Identify distances:
- The shortstop is 30 feet from second base. This means she is 60 feet from third base along the baseline (since the distance from second base to third base is 90 feet).
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Find her effective distance:
- The shortstop is effectively standing at the coordinates of 30 feet from second base (in the direction towards third) and needs to throw to first base which can be visualized as a horizontal throw from her position.
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Using the Pythagorean theorem:
- Set the coordinates:
- Second base: (0, 0)
- Third base: (0, 90)
- First base: (90, 0)
- Shortstop's coordinates after 30 feet: (0, 30)
- Calculate the distance to first base:
\[ d = \sqrt{(90 - 0)^2 + (0 - 30)^2} = \sqrt{90^2 + (-30)^2} = \sqrt{8100 + 900} = \sqrt{9000} \]
- Set the coordinates:
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Calculate: \[ \sqrt{9000} = 30 \sqrt{10} \approx 30 \times 3.1623 \approx 94.9 \]
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Final distance: Thus, rounding to the nearest tenth, the distance the shortstop needs to throw the ball is:
\[ \boxed{94.9} \text{ feet} \]
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