Question

City A and city B are approximately a=350 miles apart on the surface of the earth. Assuming that the radius of the earth is 4000 miles, find the radian measure of the central angle with its vertex at the center of the earth that has city A on one side and city B on the other side.

Answer 1

so... notice the picture below, the arc is 350 miles long,
and the radius is 4000


`\bf \textit{arc's length}=s=\theta r\implies \cfrac{s}{r}=\theta\qquad \begin{cases} \theta=\textit{angle in radians}\\ r=radius \end{cases}`