• Jan 22nd 2006, 06:02 AM
mathAna1ys!5
Earth has been charted with vertical and horizontal lines so that points can be named with coordinates. The horizontal lines are called latitude lines. The equator is latitude line 0 degrees. Parallel lines are numbered up to 90 degrees to the north and to the south. The length of any parallel of latutude is equal to the distance around Earth times the cosine of the latutude angle, if we assume a spherical Earth.

a. If the radius of Earth is about 6400 km, which latitude lines are 5543 km long?

b. What is the length of the 90 degree parallel? Why?
• Jan 22nd 2006, 06:19 AM
jacs
5543 = 2 x ∏ x 6400 x cos a
cos a = 0.1378
a = 82

so it woudl be the 82°N and the 82°S (this is approx since i have rounded)

the 90 parallel, which are the two poles (and they are points, having no distance) is zero and this is becasue it woudl be of this form

L = 2 x ∏ x 6400 x cos 90 and cos 90 = 0

hope that is what you are after
jacs
• Jan 22nd 2006, 06:40 AM
earboth
Quote:

Originally Posted by mathAna1ys!5
The horizontal lines are called latitude lines. The equator is latitude line 0 degrees. Parallel lines are numbered up to 90 degrees to the north and to the south. The length of any parallel of latutude is equal to the distance around Earth times the cosine of the latutude angle, if we assume a spherical Earth.

a. If the radius of Earth is about 6400 km, which latitude lines are 5543 km long?

b. What is the length of the 90 degree parallel? Why?

to a)
Those latitude lines have the form of a circle. So you have first to know the radius of the given perimeter:

$2\pi r=5543\ \Longleftrightarrow \ r=\frac{5543}{2\pi} \approx 882.2 km$

As I've tried to demonstrate you can draw right triangle using the radius of earth (R) and the radius of your latitudinal circle (r) and than you are able to calculate the latitude in degrees:

(Apparently I made a severe mistake in using LATEX-script, so I've to write my answer in simple typing. Awfully sorry for you!)

cos(lambda) = r / R will come up with lambda = 82.08°

to b)

The answer is zero, because you are now on one of the poles.

Bye