Math (trigonometry)
posted by Sammy .
A baseball diamond is actually a square with each side approximately 27.4 m. The pitcher's mound is 18.4 m from home plate on the diagonal of the square  note that the pitcher's mound is NOT located at the centre of the diamond!
a) How far (to 3 decimal places) from the centre of the diamond is the pitcher's mound? Is it closer to home plate or second base?
I don't know if it's that my diagram is awry or what, but I can't seem to get the answer. I don't know how easily one might be able to understand this without the diagram I drew, but here's my math:
(I made x the distance from one corner of the square/diamond (H for home plate) to the centre of the diamond. The 45° was not exactly given, but I assumed it since it's a square...)
Find x:
cos45° = 27.4 m / x
x = 27.4 m / cos45°
x = 38.7
38.7 m  18.4 m = 20.3 m therefore, the pitcher's mound is 20.3 m from the centre of the diamond.
The answer should be 0.975 m, way off.

should have been
cos 45 = x/27.4, you have it upside down, cos ? = adjacent/hypotenuse
x = 27.4(cos45) = 19.3747
so the centre is 19.3747 ft from home
making the pitcher mount 19.3747  18.4 or
.9747 ft from the centre, and being closer to home than 2nd base.
BTW, you should have know that your answer could not be correct, since entire distance from home to 2nd is ...
d^2 = 27.4^2 + 27.4^2
d = √1501.52 = 38.75 ft , which would have put your pitching mount beyond 2nd base in the outfield. 
I think I may need to rethink this question because in the diagram I drew, 27.4 m is adjacent to the 45° angle.
And the proof you showed me at the end cannot be visualised in my diagram.. Would it be possible for you to explain in words (I know it's really hard..) what your diagram looks like? 
Oh, never mind about not being able to visualise your proof at the end, I completely misread that, wow. But my diagram is still incorrect somehow because 27.4 is the adjacent side..

Oh! Wait, sorry, again. Never mind. That was really stupid of me. I don't know how I didn't see it, but I realise what was wrong now, thank you

the baseball diamond is a square with sides 27.4
If you draw the two diagonals, they will meet at the centre, giving you 4 identical rightangled triangles.
in each of these triangles 27.4 is the hypotenuse and the line going to the centre is the adjacent.