1. The Earth Question (Latitude)

The circumference of a circle of latitude is two thirds of the circumference of the equator. What is the latitude?

A diagram would be nice

2. Equator: $2\pi\;r_{e}$

New Lattitude: $2\pi\;r_{new}\;=\;\frac{2}{3}\;2\pi\;r_{e}$

$r_{new}\;=\;\frac{2}{3}r_{e}$

A right triangle: $\cos(lattitude)\;=\;\frac{r_{new}}{r_{e}}$