I don't know much beyond high school trigonometry, but I recently learned that the cosine of a line of latitude tells you its length: for e.g. the cosine of 60 degrees North (where British Columbia becomes the Yukon, 2/3 of the way from the equator to the North Pole...) is 0.5, which means that the length of that latitude is 0.5x the length of the equator. So it's about 20,000 km.
Could somebody explain to me why this is the case? I thought it might have something to do with a right triangle that goes from the centre of the earth to the pole to the equator, but I can't quite get my head around it. Thanks.