SOLUTION: Hi, I'm having some trouble trying to figure out this problem. Memphis, Tennessee, and New Orleans, Louisiana, lie approximately on the same meridian. Memphis has latitude 35 deg

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Question 129500This question is from textbook Algebra and Trigonometry
: Hi, I'm having some trouble trying to figure out this problem. Memphis, Tennessee, and New Orleans, Louisiana, lie approximately on the same meridian. Memphis has latitude 35 degrees N and New Orleans, 30 degrees N. Find the distance between these two cities. (The radius of the earth is 3960 mi.) If you could help me I'd be very grateful. Thank you. This question is from textbook Algebra and Trigonometry

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Just picture this problem like you would a slice of pie.
.
The pointed tip of the slice is where the center of the pie was. Therefore, it compares
to the location of the center of the Earth. The sliced sides of the piece of pie are like
two radii of the Earth. And the curved outer edge of the crust is like the curvature of
the Earth's surface and the length of this curved edge of the crust represents the distance
between New Orleans and Memphis. The central angle of the pie slice (vertex is the point of the slice
and the two sliced sides form the angle) is 35 degrees minus 30 degrees or 5 degrees.
.
That's a picture of what's going on. The circumference of the whole pie (or Earth) can
be found from the formula:
.
C+=+2%2Api%2AR
.
Where R is the radius of Earth, and C is the distance around the entire Earth. Substituting
3960 for R you get that the circumference of the entire Earth (or pie) is:
.
C+=+2%2Api%2A3960+=+24881.41 miles
.
But we are not interested in the full 360 degree circumference. We are only interested
in 5 degrees out of 360 degrees around the Earth. The ratio of 5 degrees to 360 degrees is:
.
5%2F360+=+1%2F72
.
The entire circumference of the Earth is 24,881.41 miles and we only want one -seventy second (1/72)
of that amount. Therefore to get the distance from New Orleans to Memphis we need only
multiply 24,881.41 by 1/72 ... the same as dividing 24,881.41 by 72 ... and we get that
the distance is about 345.6 miles.
.
Maybe the analogy of the pie slice and an Earth slice is a little confusing. Hope not. I
was just trying to give you something to visualize so that you could sort of picture what
is going on. Hope this helps you to understand the problem a little better.
.