Question

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° N, are 486 km apart.
a)38.8 N b)39.5 N c)47.5 N d)52.46 N

Please explain the awnser

Answer 1

Explanation:

Okay, let's think through this step-by-step:

- Spokane, WA and Jordan Valley, OR lie on the same north-south line

- Jordan Valley is at 43.15° N latitude

- The two cities are 486 km apart

- Radius of Earth is 6400 km

- We can use the radius of Earth and the distance between the cities to find the angle between them:

- Circumference of Earth = 2πr

- So for every 1° of latitude, the distance is:

(Circumference/360) = (2πr/360)

- Plugging in the radius as 6400 km, the distance per degree of latitude is approximately 111 km

- Jordan Valley is at 43.15° N

- The cities are 486 km apart

- To get the latitude of Spokane:

- Distance between cities (486 km) / distance per degree (111 km/degree)

- 486 km / 111 km/degree = 4.38 degrees

- So if Jordan Valley is 43.15° N, and Spokane is 4.38 degrees south of it, then:

- Spokane must be at 43.15 - 4.38 = 38.77° N

Therefore, the latitude of Spokane is approximately 38.8° N.

So the answer is A. Let me know if this explanation makes sense!