In a baseball game, baseball dimond is a square with sides 27m. how far does the first player have to throw the ball to get a runner out a third base.

The answer to this is that the first baseman must throw
38.18 meters, if he is on first base, to a person standing on the third base bag.  This
can be found by using the Pythagorean Theorem.

If you draw
out a diagram of the baseball diamond, you will see that the baselines from home to
third and home to first make a right angle at home plate.  This means that a line from
third to first is the hypotenuse of a right triangle.

The
two legs of the triangle are each 27 meters. 
Therefore:

27^2 + 27^2 = c^2 (the distance from 1st to
3rd).

1458 = c^2

c =
38.18