Calculating Distances Along Latitudes on Earth

[DS2C]

Homework Statement

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

Homework Equations

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.

 

[DS2C]

Image of work

 

[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.

 

[Chestermiller]

What is the latitude of the North Pole?

 

[DS2C]

What is the latitude of the North Pole?

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

 

[Chestermiller]

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

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

 

[DS2C]

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

47 degrees. So would I continue as:

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

 

[Chestermiller]

47 degrees. So would I continue as:

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

Do you really need to ask?

 

[DS2C]

Do you really need to ask?

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.