Aslow pitch softball diamond is actually a square 60 ft on a side. how far is it from home to second base?

For this case we have a square whose sides are known and equal to 60 ft.
 We want to find the diagonal of the square.
 For this, we use the Pythagorean theorem.
 We have then:
 
 
 from home to second base it is about:
 

We require the congruence between another pair of corresponding angles to say that those triangles are similar by the Angle-Angle Postulate.

Step-by-step explanation:

To prove that the two triangles similar we can use these postulates:

Angle-Angle Postulate: if two pairs of corresponding angles between two triangles are congruent, then, those triangles are similar.Side-Side-Side Postulate: if all corresponding sides between two triangles are proportional, or they are in a same proportion, then, those triangles are similar.Side-Angle-Side Postulate: If two pairs of corresponding angles are proportional, and one pair of corresponding angles (which are formed by the proportional sides) are congruent, then, those triangles are similar.

So, in the problem, we know that one pair of corresponding triangles are congruent. Now, we require the congruence between another pair of corresponding angles to say that those triangles are similar by the Angle-Angle Postulate. That's the shortest way.