Find the distance expalin fully please

Question

Find the distance along an arc on the surface of the earth that subtends a central angle of 1 minutes (1 minute = 1/60 degree). The radius of the earth is 3960 miles. Round to the thousandths. (3 decimal places)

Your answer is____    miles.

Answer 1

an arc length = radius times the angle (when measured in radians)

L = 3960x the angle (1/60 degree when converted to radians)

180 degrees = pi radians

1 degree = pi/180 radians

1/60 degree = pi/60(180) radians

L= 3960pi/60(180) =66pi/180 = about 1.152 miles

L= 0.3666.... miles, a little over 1/3 of a mile

or calculate the circumference = 2pi(3960) and multiply by 1/60(360)

L=2pi(3960)/21600= about 1.152 miles

Answer 2

C = 2πr

C = 2π(3960)

1 minute of arc is 1 / 3600 of the circumference C.