Answer: 8 miles
Step-by-step explanation: If we drew out the problem we would get a right triangle where d is the hypotenuse and the 16 miles south and the 12 miles east would be the legs of such a triangle. Then using the Pythagorean theorem we get:
[tex]d^2=16^2+12^2=400[/tex]
If we then take the square root of both sides we get:
[tex]d=\sqrt{400} =20[/tex]
Then we realize that the pilot was forced to travel 8 extra miles because
[tex](16+12)-20=28-20=8[/tex]
