Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-Find the latitude of Spokane, WA if Spokane and Jordan Valley, OR, $43.15 ^ { \circ } \mathrm { N }$, are $486 \mathrm {~km}$ apart.
A) $38.8 ^ { \circ } \mathrm { N }$
B) $39.5 ^ { \circ } \mathrm { N }$
C) $47.5 ^ { \circ } \mathrm { N }$
D) $52.46 ^ { \circ } \mathrm { N }$

Question

Quizplus · Accepted Answer

The distance between two points on the same meridian (north-south line) can be calculated using the formula $d = r \cdot \Delta \theta$, where $d$ is the distance, $r$ is the radius of the Earth, and $\Delta \theta$ is the difference in latitude in radians. Given that Spokane and Jordan Valley are 486 km apart and the radius of the Earth is 6400 km, we first convert the distance to radians: $\Delta \theta = \frac{d}{r} = \frac{486}{6400}$ radians. To find the difference in latitude in degrees, we convert from radians: $\Delta \theta_{\text{degrees}} = \frac{486}{6400} \times \frac{180}{\pi}$. The latitude of Jordan Valley is $43.15^\circ N$. To find the latitude of Spokane, we add the difference in latitude to the latitude of Jordan Valley if Spokane is north of Jordan Valley. The calculation shows that Spokane is approximately $4.35^\circ$ north of Jordan Valley, making its latitude approximately $43.15^\circ N + 4.35^\circ = 47.5^\circ N$.

Assume That the Cities Lie on the Same North-South Line 43.15∘N43.15 ^ { \circ } \mathrm { N }43.15∘N

Assume That the Cities Lie on the Same North-South Line $43.15 ^ { \circ } \mathrm { N }$