Earth's circumference

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

Correct answer:

x =  26728.1018 km

Step-by-step explanation:

$$\begin{gathered} R=6378\text{ km } \\ \alpha =48{\displaystyle \frac{10}{60}}=48+{\displaystyle \frac{10}{60}}={\displaystyle \frac{48\cdot 60+10}{60}}={\displaystyle \frac{2890}{60}}={\displaystyle \frac{289}{6}}\doteq 48.1667\text{ ° } \\ \cos \alpha =r\mathrm{/}R \\ r=R\cdot \cos \alpha \mathrm{°}=R\cdot \cos 48.1666666667\mathrm{°}=6378\cdot \cos 48.1666666667\mathrm{°}=6378\cdot 0.666966=4253.90952\text{ km } \\ x=2\pi \cdot r=2\cdot 3.1416\cdot 4253.9095=26728.1018\text{ km}=2.673\cdot 10^4\text{ km} \end{gathered}$$

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