The length of the arc between L A and Miami = 2700 miles
length of arc = r*c where c is in radians
2700 = 3960 * c
c = 2700/3960 = 0.68182 radians+
The tangents from the satellite to the 2 points on the earth make a 90 degree angle with the radii of the earth, so we have 2 right angled triangles with one angle = 1/2 * 0.68182 = 0.34091 radians and the hypotenuse is the distance from center of the earth to the satellite.
if x is the distance of the satellite from the surface of the earth we have the equation
cos 0.34091 = 3960 /( x + 3960)
cos 0.34091(x + 3960) = 3960
x = (3960 - cos0.3409* 3960) / cos0.34091
= 241.8 miles Answer
