Answer:
1.152 miles
Explanation:
Given: central angle = 1 minute = [tex](\frac{1}{60}) ^{o}[/tex]
radius of the earth = 3960 miles
The length of an arc = [tex]\frac{\alpha }{360^{o} }[/tex] 2[tex]\pi[/tex]r
where: [tex]\alpha[/tex] is the central angle, and r is the radius.
Thus,
Distance along the arc = [tex]\frac{\alpha }{360^{o} }[/tex] 2[tex]\pi[/tex]r
Distance along the arc = [tex]\frac{(\frac{1}{60}) ^{o} }{360^{o} }[/tex] x 2 x [tex]\frac{22}{7}[/tex] x 3960
= [tex]\frac{(\frac{1}{60}) ^{o} }{360^{o} }[/tex] x 24891.4286
= 1.1524
The required distance along an arc is 1.152 miles.
