# Geometry Problem- Latitudes

1. Dec 18, 2017

### DS2C

1. The problem statement, all variables and given/known data
Suppose your location has a latitude of 43 degrees and the circumference of the Earth is 40,000 km. Measure the distance from your location along a circle. How far would you have to travel if you go a) to the equator, and b) to the North Pole

2. Relevant equations

3. The attempt at a solution
For part "a" I got about 4,777 km. But not sure how to go about part "b". I need the a new latitude but not sure how to get it. I originally thought about subtracting 43 degrees form 360 degrees, but that seems way too big as it's the whole circumference of the Earth minus the portion from problem "a".
Please see attached image. I need to find angle NOT I think.

2. Dec 18, 2017

### DS2C

Image of work

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3. Dec 18, 2017

### DS2C

Actually I think I might have it. If I separate it into four quadrants, E to N would be 90 degrees. Which would make T to N 47 degrees.

4. Dec 18, 2017

### Staff: Mentor

What is the latitude of the North Pole?

5. Dec 18, 2017

### DS2C

This is my first tussle with latitudes etc. But from my previous post, I will be willing to bet it's 90 degrees.

6. Dec 18, 2017

### Staff: Mentor

So how many degrees of latitude are there between 43 N and the North Pole?

7. Dec 18, 2017

### DS2C

47 degrees. So would I continue as:

[(47/360) x 40,000] / (360) = 5222 km approximately?

8. Dec 18, 2017

### Staff: Mentor

Do you really need to ask?

9. Dec 18, 2017

### DS2C

I got that part since it was done the same was as problem "a". The part that I was unsure about was finding the second latitude as I was originally subtracting the given from 360. I got it now. Thanks for your reply sir.