Earth parallel

Earth's radius is 6377 km long. Calculate the length parallel to latitude 75°.

Correct answer:

l =  10370 km

Step-by-step explanation:

Φ=75° rad=75° π180 =75° 3.1415926180 =1.309=5π/12  R=6377 km  r=R cos(Φ)=6377 cos1.3091650.4891 km l=2π r=2 3.1416 1650.4891=10370 kmΦ = 75 \degree \rightarrow\ \text{rad} = 75 \degree \cdot \ \dfrac{ \pi }{ 180 } \ = 75 \degree \cdot \ \dfrac{ 3.1415926 }{ 180 } \ = 1.309 = 5π/12 \ ^\circ \ \\ R = 6377 \ \text{km} \ \\ \ \\ r = R \cdot \ \cos(Φ) = 6377 \cdot \ \cos 1.309 \doteq 1650.4891 \ \text{km} \ \\ l = 2 \pi \cdot \ r = 2 \cdot \ 3.1416 \cdot \ 1650.4891 = 10370 \ \text{km}



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solid geometryplanimetricsgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem

 
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