## A latitude and longitude question

A friend of mine, a geography teacher, tweeted me this question earlier:

A lovely set of questions that I thought I’d run through here. I hope you’ve had a go at them before you read on….

The first one appeared at first to be a very simple question, just looking at the proportion of the circumference you have travelled. I then noticed the sleight of hand with the units and realised it involved an extra step. Still relatively straightforward though. Convert the distance from miles to km and work out the proportion of the circumference you have travelled. Multiply that by 36o and you have your angle, in this case 50.57 degrees to 2dp.

The second question is more tricky. The first thing we need to work out is the radius of the circle we would get if we cut a cross section parallel to the equator 30 degrees north. In order to do this I drew a diagram (always imperative! ).

This allowed me to find a right angled triangle with the hypotenuse being the radius of the earth. This allowed me to find the radius of the circle I was after.

Once I had this I could work out the distance travelled easy enough, as we have travelled 180 degrees so half the circumference.

Or 15349 km (to the nearest km.) Here I’m assuming we want the distance we have travelled around the earth, rather than the displacement which would obviously be the diameter of the cross section or 9772km.