Find the distance along an arc on the surface of Earth that subtends a central angle of 5 minutes (1 minute=160 degree). The radius of Earth is 3960 miles.
as always,
s = rθ = 3960 * (5/60 * π/180) = 11π/6 km
s=rθ
(1/6)(pi/180) ... this turns 1 minute worth of degrees into radian
= pi/10800 multiply by 5 for the five minutes
5pi/10800 ...simplify... pi/2160
plug into formula
s = (3960)*(pi/2160)
s = 3960pi/2160 ...simplify...
s = 11pi/6 ≈ 5.76 mi