You have to add (or subtract, depending which point is on West side) the following:
distance_in_meters/Earth_radius_in_meters/cos(lat)*360degree/2/pi
or, alternatively:
distance_in_meters/Earth_equator_length_in_meters/cos(lat)*360degree
This works because the radius of circle of 'slice of Earth' (more precisely, intersection of Earth and plane perpendicular to Earth's axis, passing through point A), is equal to radius of Earth * cos(lat) - simple trigonometry. Then you just use the proportions:
360 degrees - 2pi R cos(lat)
x degree - d meters
x=360d/2/pi/R/cos(lat)
This is all assuming you use degrees.