Question 1068203
R^2+D^2=(R+4)^2, where R=4000 miles. Draw it and there is a right triangle with the legs the Earth's radius and the line of sight from the Earth to the plane.  The hypotenuse is from the plane to the center of the Earth.
4000^2+D^2=4004^2
D^2=16032016-16000000=32016
D=sqrt (32016)=178.93 miles, round to 180 miles.