Earth Geometry circumference of the latitude

Question

Calculate the circumference of latitude 60°South as a percentage of the circumference of the earth take R=6370km

Answer 1

Drawing the earth as a circle and the latitude as the angle from the equator, we see that the result is a 30-60-90 triangle where the hypotenuse is the radius of the earth and the short side is the radius of the circle of the 60° south latitude. The short side of a 30-60-90 triangle is 1/2 of the hypotenuse so it is 1/2(6370 km).

The circumference at the 60° S latitude circle is 2πr = 2π(1/2(6370 km)) = 6370π. The circumference at the equator is 2πr = 2π(6370) so the ratio of the two is 6370π/2π(6370) = 1/2 = 50%