Major League baseball diamond is actually a square on a side.

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

(a) Find the distnace from the pitching rubber to first base.

Draw the related diagram.

Cosine law:

.

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

(b)

Find the distance from the pitching rubber to second base.

Apply pythagorean rule : .

.

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

(c)

Cosine law:

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

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

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

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