SOLUTION: Seward, Alaska is 180 degrees due west of St. Petersburg Russia. Both places are 60 degrees north of the equator. Calculate the distance between the two assuming a) we travel along

Algebra ->  Circles -> SOLUTION: Seward, Alaska is 180 degrees due west of St. Petersburg Russia. Both places are 60 degrees north of the equator. Calculate the distance between the two assuming a) we travel along      Log On


   

Question 1172987: Seward, Alaska is 180 degrees due west of St. Petersburg Russia. Both places are 60 degrees north of the equator. Calculate the distance between the two assuming a) we travel along the circle of latitude;
b) we travel along the circle that passes over the north pole.
Answer by ikleyn(52858) About Me  (Show Source):
You can put this solution on YOUR website!
.

(a) For case (a), the radius of the circle of latitude is one half of the Earth radius, 

    and the traveled distance is half of the circumference of this circle.


    So, the traveled distance is one fourth of the equator circumference.


    From my school years, I remember that the equator circumference is about 40,000 kilometers.


    So, the answer to this question is 


        "the travel distance is one fourth of the equator circumference, or about 10,000 kilometers".




(b) In case (b), the circle is a large circle of the Earth sphere, and the traveled distance is  one sixth of its circumference.


    So, the answer in this case is 


        "the travel distance is one sixth of the equator circumference, or about %281%2F6%29%2A40000 kilometers = 6,666 kilometers".


Thus we revealed that the route through the  North pole is shorter in this case than along the altitude  (!)


It may seem unexpected,  but it is  TRUE  (!) 

    Probably,  I will surprise you  EVEN  MORE,  if I say that the route through the  North  Pole 

    is the  SHORTEST  route on the  Globe between the given points in this case (!) (!) (!)

    It is,  probably,  EVEN  MORE  unexpected,  but it is  TRUE,  again.


Come again to this form soon to learn something new  (!)