Final answer:
At 45 degrees north or south, the distance between longitudes is approximately 48.8 miles, which is about 0.7071 times the distance at the equator (69 miles).
Step-by-step explanation:
The distance between longitudes at any given latitude is not a fixed measure, like it is at the equator. Since longitudes converge at the poles, the distance between longitudes decreases as one moves away from the equator towards the poles. At the equator, this distance is roughly 69 miles, which is the maximum distance. However, at 45 degrees north or south, this distance is reduced because of the geometry of the Earth. It can be calculated that at 45 degrees latitude, the circumference of the Earth is cos(45°) times the equatorial circumference. Consequently, since the cosine of 45 degrees is approximately 0.7071, the distance between longitudes would be about 0.7071 times 69 miles, which is approximately 48.8 miles.