What is the angular size of a quarter viewed from a distance of 7 yards? (A quarter is about 1 inch in diameter.)

Question

What is the angular size of a quarter viewed from a distance of 7 yards?


(A quarter is about 1 inch in diameter.)

 

Can someone help me figure out the formula to answer this question? 

Answer 1

7 yards = 36x7 = 252 inches

the quarter is roughly the opposite side of a right triangle = 1 inch, with adjacent side = 252 inches

tangent of the angle = 1/252

the angle = about 0.227 degrees

but it's not exactly a right triangle. it's the chord of a sector of a circle, a very slim sector. the arc length = radians time radius = 1 inch = 262A where A= the angle measured in radians A=1/262 = 57.3/262 = 0.22 degrees = .22(60 = 13.2 minutes= 13 minutes and 12 seconds. 1 degree=60 minutes 1 minute = 60 seconds

formula for the length of a chord = 2rsin(A/2)

1 inch = 2(262)sin(A/2)

sin(A/2 = 1/524

A = about 0.219 degrees = a little less than using 1 inch as the arc length or opposite side of a right triangle. As the chord length of 1 inch at 7 yards, the angle is 0.219 degrees.