Final answer:
The linear distance between two points on a meridian can be calculated by dividing the given mileages by 69 to find the equivalent degrees of latitude, then finding the difference in degrees and multiplying by 69 to get the distance in miles.
Step-by-step explanation:
To calculate the linear distance in miles between points on a meridian using degrees of latitude, you can use the approximate value of 69 miles for each degree of latitude. This distance is a straight line, or 'linear' distance, as opposed to the distance along the surface of the Earth (which would be a geodesic distance).
The question seems to provide distances in miles that possibly correspond to differences in latitude. However, without specific starting and ending latitudes or the context of how these mileages were obtained, we cannot directly calculate the linear distance between two latitudes by simply using these values. It is likely that these values should correspond to changes in latitude (difference in degrees), in which case we would calculate the degree equivalent by dividing by 69 (since 69 miles represent one degree of latitude) and then use that result to find the linear distance in miles between the two latitudes.
For example, if a point is 2430 miles from the equator, the equivalent in degrees of latitude would be 2430 / 69 = 35.22 degrees. To find the distance between two points, we subtract the degrees of latitude and multiply by 69. If another point is 2760 miles from the equator (equivalent to 2760 / 69 = 40 degrees), the linear distance between the two points would be:
(40 - 35.22) × 69 = 4.78 × 69 = approximately 329.82 miles
This method applies to any pairs of mileages given to calculate the linear distance between points on a meridian.