Question

two cities are 2000 km apart and lie on the same north - south line. the latitude of the northernmost city is 61° n. what is the latitude of the other city? the radius of the earth is approximately 6400 km.
the latitude of the other city is approximately (square^{circ}) n
(do not round until the final answer. then round to the nearest integer as needed.)

Explanation:

Step1: Calculate the central angle

We know that the arc - length formula is $s = r\theta$, where $s$ is the arc - length (distance between the two cities), $r$ is the radius of the Earth, and $\theta$ is the central angle in radians. Given $s = 2000$ km and $r=6400$ km. Then $\theta=\frac{s}{r}=\frac{2000}{6400}=\frac{5}{16}$ radians.

Step2: Convert radians to degrees

To convert radians to degrees, we use the conversion factor $\theta_{degrees}=\theta_{radians}\times\frac{180^{\circ}}{\pi}$. So $\theta_{degrees}=\frac{5}{16}\times\frac{180^{\circ}}{\pi}\approx17.9^{\circ}$.

Step3: Find the latitude of the other city

Since the two cities are on the same north - south line and the northernmost city has a latitude of $61^{\circ}N$. If the other city is south of the northernmost city, the latitude of the other city is $61^{\circ}-\theta_{degrees}$. So the latitude is approximately $61 - 17.9=43.1^{\circ}N\approx43^{\circ}N$.

Answer:

$43$