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City A is due north of City B. Find the distance between City A ​(36 degrees 6 prime36°6′ north​ latitude) and City B ​(21 degrees 42 prime21°42′ north​ latitude). Assume that the radius of Earth is 3960 miles. The distance between City A and City B is how many miles?

Respuesta :

Answer:

distance = 994.75 miles

Step-by-step explanation:

given data

City A = 36°6′ = 36° + [tex]\frac{6}{60}[/tex] = 36.1° = 36.1° × [tex]\frac{\pi}{180}[/tex] = 0.6297 rad

City B = 21°42′ = 21° + [tex]\frac{42}{60}[/tex] = 21.7° = 21.7° × [tex]\frac{\pi}{180}[/tex] = 0.3785 rad

multiply by π/180 to convert the degree to radian

radius of Earth = 3960 miles

to find out

distance between City A and City B

solution

we first get here central angle between A and B city is

central angle between A and B city = 0.6297 rad - 0.3785 rad

and

now by arc length so  we get distance

distance = 3960 miles × (0.6297 rad - 0.3785 rad )

distance = 994.75 miles

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