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HINT:Lets consider first what the question is asking.
The question is asking for a distance between two points along the surface of the earth that have the same longitude.
HINT:What information does the problem give us?
The location of two points in degrees latitude and degrees longitude.
HINT:What is the relationship between the information given and the
information needed?
The length of an arc of radius r (variables in bold)
A = (2r)pi * (# degrees in the arc/360)
HINT:What information do we need to plug into the relationship?
pi = 3.1416 (Sourced from calculator, rounded to one more specific digit than the piece of information than the radius of the earth.)
r = radius of arc on the surface the earth = rearth =6378 km
(# degrees in the arc/360) = by looking at the picture next to the question we intuitively know what we will walk along half of any great circle connecting the North and South poles. Let's compute the number of degrees between the poles mathematically:
# degrees in arc = lat2 - lat1 = (90 N) - (90 S). In order to subtract these two numbers, they must be expressed in terms of the same units - we may remember that (1) degree South is equal to (-1) degree North, so (90 S) = (-90 N)
lat2 - lat1 = (90N) - (-90N) = 90 N + 90 N = 180 deg.
HINT: Are we going to need to convert the units of any of the information that
we have gathered?
Let's use unit analysis:
A = 2(km)(circumference (km)/diameter (km))*(deg./deg.)
All units cancel except for km, so A will be in km, the unit for distance appropriate to the problem.
HINT:Plug all of the information in to the final calculation!
A = 2(6378 km)(3.1416) * (180/360) = 20,037 km

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