Use Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]
We have
a = 3959 mi
b = x
c = 3959 mi + 5.9 mi = 3964.9 mi
Substitute:
[tex]3959^2+x^2=3964.9^2\qquad\text{subtract}\ 3959^2\ \text{from both sides}\\\\x^2=3964.9^2-3959^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\x^2=(3964.9-3959)(3964.9+3959)\\\\x^2=(5.9)(7923.9)\\\\x^2=46751.01\to x=\sqrt{46751.01}\\\\x\approx216.2[/tex]
Answer: 216.2 mi.
