A circle is divided into 360 degrees -- this was developed by the ancient Babylonians.
Later as more precision was required, Europeans divided a degree into 60 tiny parts, calling them partes minutes -- hence our term "minute." Hours of time were also divided that way, so we make sure people understand we are talking about angular measurement by using the term "minute of angle."
There are 21,600 (360 X 60) minutes of angle in a circle.
Since the circumfrence of a circle is calculated by the formula C = Pi * D, if we take a circle with a 100 yard radius (200 yard diameter) and convert that to inches (200 * 36 = 7,200), we get a circumfrence of 3.1416 * 7,200 = 22,620 inches.
So we see a minute of angle subtends about 22,620/21,600 or 1.0472 inches.
(just in passing, I might note that both minutes of time and minutes of angle were further divided into 60 partes minutes secondes, or "seconds.")