Question

two cities have nearly the same north - south line of 104° w. the latitude of the first city is 23° n,and the latitude of the second city is 35° n. approximate the distance between the cities if the average radius of earth is 6400 km. the cities are approximately kilometers apart. (round to the nearest integer as needed.)

Explanation:

Step1: Calculate the central - angle

The difference in latitudes gives the central - angle $\theta$ between the two cities. $\theta=(35 - 23)^{\circ}=12^{\circ}$. Convert degrees to radians. Since $1^{\circ}=\frac{\pi}{180}$ radians, then $\theta = 12\times\frac{\pi}{180}=\frac{\pi}{15}$ radians.

Step2: Use the arc - length formula

The formula for the length of an arc $s$ of a circle with radius $r$ and central - angle $\theta$ (in radians) is $s = r\theta$. Here, $r = 6400$ km and $\theta=\frac{\pi}{15}$ radians. So, $s=6400\times\frac{\pi}{15}=\frac{6400\pi}{15}\approx\frac{6400\times3.14159}{15}$.

Step3: Calculate the value

$\frac{6400\times3.14159}{15}=\frac{20096.176}{15}\approx1339.745$.

Answer:

1340