Two cities in the western hemisphere lie approximately on the same meridian. City A has latitude of $15.5 ^ { \circ }$ N and City B, $60.5 ^ { \circ }$ N. Find the distance between these two cities. (The radius of the earth is $3960$ Miles.)
A) $3,960 \text { miles }$
B) $3,110 \text { miles }$
C) $3,250 \text { miles }$
D) $2,110 \text { miles }$
E) $5,280 \text { miles }$

Question

Quizplus · Accepted Answer

The distance between two points on the same meridian can be calculated using the formula $d = \pi r \frac{| \theta_1 - \theta_2 |}{180}$, where $d$ is the distance, $r$ is the radius of the Earth, and $\theta_1$ and $\theta_2$ are the latitudes of the two points. Here, $r = 3960$ miles, $\theta_1 = 15.5^\circ$, and $\theta_2 = 60.5^\circ$. Plugging these values into the formula gives $d = \pi \times 3960 \times \frac{|15.5 - 60.5|}{180} = \pi \times 3960 \times \frac{45}{180} = 22\pi \times 110 = 3,110$ miles.

Two Cities in the Western Hemisphere Lie Approximately on the Same