how far is it across the field is it from third to first, and what is the equation to figure it ?

Answer 1

a baseball diamond is just a big square

and all sides are 90 feet

so you can use the Pythagorean theorem
2 2 2
which is A + B = C

A and B being 90, and C being the distance from 1st to 3rd

the answer turns out to be 127.279 ft

Answer 2

I'm guessing you're talking about baseball, a major league field (and normal measurement for kids 16 and up) is 90 feet from first to second, 90 from second to third, etc. etc.
Using the pythagorean theroem a^2+b^2=c^2 to solve
90^2+90^2=c^2
c=127.3 ft

Answer 3

Use the Pythagorean theorem.
a^2 + b^2 = c^2

c = (a^2 + b^2)^0.5

In this case a = b

the distance from home to first and
the distance from home to third.

so you have c = (2a^2)^0.5

the distance from first to third will be the hypotenuse (c).