SOLUTION: Latitude gives the measure of the central angle (vertex at center of earth) whose initial side is the equator and whose terminal side goes through the given angle location. The rad

Algebra ->  Trigonometry-basics -> SOLUTION: Latitude gives the measure of the central angle (vertex at center of earth) whose initial side is the equator and whose terminal side goes through the given angle location. The rad      Log On


   

Question 1109444: Latitude gives the measure of the central angle (vertex at center of earth) whose initial side is the equator and whose terminal side goes through the given angle location. The radius of the earth is 6400 km. If Town A is located at latitude 42 degrees N directly north of Town B which is at latitude 15 degrees S, how far apart are the towns? Round to the nearest kilometer.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!

the equator is at at latitude 0 degrees.

town A is at latitude 42 degrees north.

town B is at latitude 15 degrees south.

this makes the angle between them equal to 42 + 15 = 57 degrees.

they both have the same longitude because they are directly north or south of each other.

town A is 57 degrees directly north of town B.

town B is 57 degrees directly south of town A.

the radius of the earth is 6400 kilometers.

the circumference of the earth if 2 * pi * 6400 = 40212.38597 kilometers.

the distance between the towns is an arc on the circumference of the earth whose central angle is 57 degrees.

the formula for the length of an arc is equal to central angle of the arc divided by 360 * circumference of the circle.

this makes the distance between the two towns equal to 57/360 * 2 * pi * 6400 which make it equal to 6366.961111 kilometers.

that should be your solution.

here's a reference on latitude and longitude.

https://www.geovista.psu.edu/grants/MapStatsKids/MSK_portal/concepts_latlg.html

here's my diagram of what i think is happening.

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