Solve the problem.
-A ship in the Atlantic Ocean measures its position to be 30°48' north latitude. Another ship is reported to be due north of the first ship at 41°17' north latitude. Approximately how far apart are the two ships? Round to the
Nearest mile. Assume that the radius of the Earth is 3960 miles.
A) 725 mi
B) 75,966 mi
C) 75,991 mi
D) 1,351 mi

Question

Quizplus · Accepted Answer

The distance between two points on the Earth's surface, measured along the surface of the Earth, can be calculated using the formula for the arc length of a circle, $s = r\theta$, where $s$ is the arc length, $r$ is the radius of the circle (in this case, the Earth's radius), and $\theta$ is the central angle in radians. The difference in latitude between the two ships is $41°17' - 30°48' = 10°29'$. Converting this to decimal degrees gives approximately $10.483°$. Converting degrees to radians (since $1° = \frac{\pi}{180}$ radians), we get $\theta \approx 10.483 \times \frac{\pi}{180} \approx 0.183$ radians. Plugging into the arc length formula with $r = 3960$ miles, we get $s \approx 3960 \times 0.183 \approx 725$ miles.

Solve the Problem. -A Ship in the Atlantic Ocean Measures Its Position to Its