Trig - Using cosine/sine rule - finding the distance between two points on a triangle with 2 sides given, with no angle given

Question

A baseball diamond is a square 90 feet on a side, and the pitcher’s mound is 60.5 feet from Home Plate. How far is it from the mound to First Base? 

I'm really confused about how to do this because only 2 sides are given, with no angle. 

Answer 1

While the included angle between the two given sides is not "given" it can be deduced by remembering that the diagonal from home plate to second base passes through the pitcher's mound and that diagonal makes a 45 degree angle with the side from home plate to first base. Now you can apply the law of cosines to solve the problem. Proceed!