Earth's circumference

Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.

Correct result:

x =  26728.102 km

Solution:

R=6378 km A=48+10/60=289648.1667   cosA=r/R  r=R cosA=R cos48.1666666667 =6378 cos48.1666666667 =6378 0.666966=4253.90952  x=2π r=2 3.1416 4253.9095=26728.102 kmR=6378 \ \text{km} \ \\ A=48+10/60=\dfrac{ 289 }{ 6 } \doteq 48.1667 \ ^\circ \ \\ \ \\ \cos A=r/R \ \\ \ \\ r=R \cdot \ \cos A ^\circ =R \cdot \ \cos 48.1666666667^\circ \ =6378 \cdot \ \cos 48.1666666667^\circ \ =6378 \cdot \ 0.666966=4253.90952 \ \\ \ \\ x=2 \pi \cdot \ r=2 \cdot \ 3.1416 \cdot \ 4253.9095=26728.102 \ \text{km}



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