Answer
a. $984\ mi$
b. $1016\ mi$
Work Step by Step
a. Using the figure in the exercise and given conditions, we have
$a=5000, b=4750, c=16, R=4000\ mi$
The distance of the Perigee above the Earth's surface can be found as
$d_1=a-c-R=5000-16-4000=984\ mi$
b. The distance of the Apogee above the Earth's surface can be found as
$d_2=a+c-R=5000+16-4000=1016\ mi$