Question

Winnipeg, Manitoba and Wichita, KS lie on the same longitudinal line. Wichita is at 38° latitude and Winnipeg is at 50° latitude. If the earth is a sphere of radius 4000 miles, use arc length to find the distance between the cities. [Use π = 3.14, and round to the nearest mile.]

Its 840 Miles

Answer 1

837 miles

Explanation:

Since they are on the same longitudinal line we can treat it just like a circle of radius 4000 miles, since the circles making of the longitude stay the same on a sphere. if they had the same latitude we would need an extra step of figuring out that particular circle's radius.

Now, on a circle of radius 4000 there is one point at 50 degrees on the circle and anther at 38 degrees, so now we find the arc length.

Arc length is basically taking a fraction of the circumference. if we went half way around the circle the arc length would be half the circumference. a tenth of the way makes a tenth of the circumference.

We go from 38 to 50 which is 12 degrees. out or 360 total this is 1/30 of the full circumference.

The circumference is 2*pi*r = 2*3.14*4000. so we want 1/30 of that, which means we divide it by 30.

2*3.14*4000/30 837.33 so to the nearest mile is just 837