Find the distance between the cities.

Question

Find the distance between the cities. Assume that Earth is a sphere of radius 4000 miles and that the cities are on the same longitude. (one city is due north of the other). (Use the formula for arc length. Round your answer to the nearest mile.)

City Latitude

Dallas, Texas 32° 47' 9'' N

Omaha, Nebraska 41° 15' 50'' N

Answer 1

The angle between them is (41° 15' 50'') - (32° 47' 9'')

Convert to radians by first converting to decimal degrees, then multiplying by (π/180)

Convert to decimal degrees: 41 + 15/60 + 50/(60•60) = 41.26389° and 32 + 47/60 + 9/(60•60) = 32.78583°

Angle between them is 41.26389° - 32.78583° = 8.47806° then, multiplying by (π/180) = 0.14797 radians

Use the equation S = rθ to find the arc length which will be the distance:

S = (4000)(0.14797) = 592 miles