I have this problem I have to solve. I am given a coordinate lat/lon, and I need to find a random point within 3 meters of this original point. Approximations are good, but all I could find was this https://gis.stackexchange.com/questions/2951/algorithm-for-offsetting-a-latitude-longitude-by-some-amount-of-meters that has a 10 meter error. Thank you.
Not sure what "find" and "random" mean in this question.
The earth is about 10 million meters from equator to either pole (that's actually how they defined the size of the meter, at first; it's been modified slightly since). The width of latitude lines doesn't vary, so one meter north or south is always is one ten-millionth of 90 degrees, or 9e-6 degrees, so just multiply that by the north-south displacement in meters of your desired point from the initial point and you'll get the number to add to the initial point in degrees: delta_lat = y_meters * 9e-6.
The width of longitude lines does vary, but it works out as simply east-west displacement in meters * 9e-6 = delta_lon * cos(lat), which means you can use the distance from your initial point to figure the east-west difference in degrees: delta_lon = x_meters * 9e-6/cos(lat).
You'll have to be careful with that last part around the poles, because cos(lat) will approach zero. Navigational systems use quaternions to do these things because they don't have singularities in spherical coordinates.