To determine how far the shortstop needs to throw the ball to first base, we can visualize the configuration of the baseball field as a square.
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Field Layout: The bases form the corners of a square, with the following points:
- Second base (point B)
- First base (point A)
- The shortstop's position (point S) is 30 ft away from second base (point B) towards third base.
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Position Calculation:
- The distance between each base is 90 ft.
- Since the shortstop is standing directly on the line between second base and third base (point S), she is 30 ft from second base (point B) and therefore:
- The distance from shortstop (S) to third base (T) is 30 ft.
- The remaining distance from second base (B) to the line of first base (A) is 90 ft.
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Using the Pythagorean theorem:
- We need to find the direct distance (d) from the shortstop's position (point S) to first base (point A).
- The horizontal distance from point S to point A is:
- \( 90 , \text{ft} \) (from B to A)
- The vertical distance from shortstop (S) to second base (B) is:
- \( 30 , \text{ft} \) (the distance she is from second base).
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Putting into the Pythagorean theorem: \[ d^2 = (\text{horizontal distance})^2 + (\text{vertical distance})^2 \] \[ d^2 = (90)^2 + (30)^2 \] \[ d^2 = 8100 + 900 = 9000 \] \[ d = \sqrt{9000} \approx 94.87 , \text{ft} \]
Thus, rounding to the nearest tenth, the shortstop needs to throw the ball approximately 94.9 ft to reach first base.
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