Find the distance between the cities. Assume that earth is asphere of radius 400

Question

Find the distance between the cities. Assume that earth is asphere of radius 4000 miles and that the cities are on the samelongitud (one city is due north of the other) Dallas,Texas            Latitude: 32° 47' 39'' N Omaha, Nebraska    Latitude: 41° 15'50'' N Find the distance between the cities. Assume that earth is asphere of radius 4000 miles and that the cities are on the samelongitud (one city is due north of the other) Dallas,Texas            Latitude: 32° 47' 39'' N Omaha, Nebraska    Latitude: 41° 15'50'' N

Explanation / Answer

***Definitions*** R = 4000 mi L1 = 32° 47' 39'' = 32.794 degrees = 0.57236 radians L2 = 41° 15' 50'' = 41.264 degrees = 0.72019 radians d = Distance L = L2 - L1 = 0.14783 radians *** Haversine Formula: haversin() = sin2(/2) h = haversine(d/R) h = haversine(L) + 0 (Because no change inlongitude) h = haversine(0.14783) h = sin2(0.073915) h = 0.005453 d = 2Rarcsin(h) d = 8000*arcsin(0.073844) d = 8000*0.73911) d = 591.29 miles

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