Help me with this question

Question

A baseball diamond is a square with sides 27.4m. The pitchers mound is 18.4m from home plate on on the line joining home plate and second base. How far is the pitchers mound from first base?

Answer 1

Here's a sketch:

We know the angle is 45 because it's on the diagonal of a square. But we do NOT know that side x hits the diagonal at 90° (in fact it does not).

We can use the Law of Cosines to solve for side "x"

x² = 18.4² + 27.4² - 2(18.4)(27.4(cos(45))

x² = 338.56 + 750.76 - 712.9899

x² = 376.33

x = 19.4 m