Answer :
The distance between the two cities on the same longitude is 731.3 miles.
How to calculate distance?
The distance between Dallas, Texas, and Omaha, Nebraska can be found using the spherical law of cosines. The formula is as follows:
d = acos(sin(lat1) x sin(lat2) + cos(lat1) x cos(lat2) x cos(long2 - long1)) x r
Where d is the distance between the two points, lat1 and lat2 are the latitudes of the two points, long2 - long1 is zero since the two cities are on the same longitude, and r is the radius of the earth (4000 miles).
Converting the latitude of each city to radians:
lat1 = 32.7944° = 32.7944 x pi/180 = 0.5718 radians
lat2 = 41.2639° = 41.2639 x pi/180 = 0.7184 radians
Inserting the values into the formula:
d = acos(sin(0.5718) x sin(0.7184) + cos(0.5718) x cos(0.7184) x cos(0)) x 4000
d = 731.3 miles
Rounding the answer to one decimal place:
d = 731.3 miles = 731.3 miles ≈ 731.3 miles
The distance between Dallas, Texas, and Omaha, Nebraska is approximately 731.3 miles.
Learn more on longitude distance here: https://brainly.com/question/28173702
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The complete question is:
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). (Round your answer to one decimal place.)
City Latitude
Dallas, Texas 32° 47' 39'' N.
Omaha, Nebraska 41° 15' 50'' N.
