Longitude, Latitude Question. Converting distance in miles to longitude and latitude

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Let's say I have some points on a map. Point one is at a longitude of -48.6 and a latitude of 38.8. Point 2 on the map is at a longitude of 52.1 and a latitude of 30.3. A line between these two points can be called A.

I would like to find 2 point along a line that is perpendicular to line A, intersecting line A at point 2, and exactly 15 miles from point 2.

Is there a way that I could go about doing this? Finding a line that satisfies the first criteria is fairly simple, but I am a bit confused on converting miles to longitude and latitude.

Any help would be greatly appreciated.