Question

this is my last problem can someone PLEASE help me:





Assuming that Earth is a sphere of radius
6378 kilometers, what is the difference in latitude of two cities, one of which is 1190 kilometers due north of the other?

Answer 1

Dude, stop reposting this question, I already answered it. Here it is again.

Lat = flat, so we're looking at East-West lines on a globe. Imagine an arrow from the center of the earth pointing to each city. What shape does this make? Roughly a triangle, right? If you neglect the curvature of the earth (is this a good assumption?), then you end up with a triangle for which you know three sides, but not the angles between them. At this point, you can invoke the law of cosines to find the angle. http://en.wikipedia.org/wiki/Law_of_cosines The angle is roughly the difference in latitude between the cities.

Answer 2

0_o do you mind elaborating. . with numbers?

Answer 3

Does something confuse you?

Answer 4

yes. the problem

Answer 5

Suppose we start anywhere along a line of longitude and start moving north, through the north pole then continue on in the same direction south through the opposite line of longitude through the south pole, then back along the original line of longitude back to where we started.

How many degrees have we swept out in the this path at the center of the earth? 360 degrees. How many radians? 2pi. If R is the radius of the earth in kms, how many kms have we moved? 2piR, the radius of the circle.

So if I started at a point on the earth and moved X kms north, then how many radians have be moved? Well, how much of a circle have we swept out? R/2piR.

Take this number now and multiply it by 360 degrees. This is the change in latitude. Clear?

Answer 6

@JamesJ Way less complicated than my explanation.

Answer 7

Thanks. Obviously the answer to the question "How much of a circle have we swept out?" is not R/2piR but X/2piR. Sorry for any confusion.