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?

distance = 994.75 miles

Step-by-step explanation:

given data

City A = 36°6′ = 36° + = 36.1° = 36.1° × = 0.6297 rad

City B = 21°42′ = 21° + = 21.7° = 21.7° × = 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

77

step-by-step explanation:

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b