$\"\"$

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Major League baseball diamond is actually a square $\"\"$ on a side.

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The pitching rubber is located $\"\"$ from home plate on a line joining home plate and second base.

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(a) Find the distnace from the pitching rubber to first baseDraw the related diagram

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$\"\"$

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Cosine law:

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Therefore, the distnace from the pitching rubber to first base is $\"\"$ .

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$\"\"$

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(b) Find the distance from the pitching rubber to second base.

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Apply pythagorean rule : $\"\"$ .

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$\"\"$

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$\"\"$ .

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Therefore, the distnace from the pitching rubber to first base is $\"\"$ .

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$\"\"$

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(c)

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Cosine law: $\"\"$

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$\"\"$

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$\"\"$ .

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Therefore, the pitcher needs to turn through an angle of $\"\"$ to face first base.

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$\"\"$

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(a) The distnace from the pitching rubber to first base is $\"\"$ .

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(b) The distnace from the pitching rubber to first base is $\"\"$ .

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(c) The pitcher needs to turn through an angle of $\"\"$ to face first base.