Solve the problem.
-Find the distance in kilometers between the cities whose latitudes are given. Assume that the cities are on a north-south line and that the radius of the earth is 6400 km. City E, 24°N and city F, 54°S
A) 8713 km
B) 8721 km
C) 3343 km
D) 3351 km

Question

Quizplus · Accepted Answer

The distance between two points on the Earth's surface, given their latitudes and assuming they lie on a north-south line, can be calculated using the formula for arc length, $s = r\theta$, where $s$ is the arc length, $r$ is the radius of the Earth, and $\theta$ is the central angle between the two points in radians. The total latitude difference between City E (24°N) and City F (54°S) is $24° + 54° = 78°$. Converting degrees to radians (since $1° = \frac{\pi}{180}$ radians), we get $78° \times \frac{\pi}{180} = \frac{78\pi}{180} = \frac{13\pi}{30}$ radians. Using the Earth's radius $r = 6400$ km, the distance $s$ is calculated as $s = 6400 \times \frac{13\pi}{30}$. This calculation gives approximately $s \approx 8713$ km, making the correct answer A.

Solve the Problem. -Find the Distance in Kilometers Between the Cities Whose Latitudes