On the​ earth, 49 degrees of latitude is how many​ kilometers? how many​ miles? (Assume that the radius of the earth is 6400​ km, or 4000​ mi, approximately.)

1 Answer
May 3, 2018

#~~5473# km; #~~3421# miles

Explanation:

Given: #r_(Earth) ~~ 6400# km #~~4000 # mi

The latitude lines run horizontally from #0@# at the equator to #+90^@# at the North Pole and #-90^@# at the South Pole. This means there are #180^@# total.

Calculate the half circumference (from South to North):

# 1/2 C = 1/2 * 2 * pi * r = pi * r_(Earth)#

In km: # " "1/2 C = 6400 pi#

In miles: # " "1/2 C = 4000 pi#

Use proportions to calculate #49^@#:

#180^@/(6400pi) = 49^@/x; " "180^@/(4000pi) = 49^@/y#

#x = (49 * 6400 pi) /180 ~~5473# km

#y = (49 * 4000 pi) /180 ~~3421# miles