Answer:
The pilot's distance to the horizon is 290.1 kilometers.
Step-by-step explanation:
Given : Earth has a radius of 6371 kilometers. A pilot is flying at a steady altitude of 6.6 kilometers above the earth's surface.
To find : What is the pilot's distance to the horizon?
Solution :
Let A is the position of the pilot which is 6.6 km above the earth's surface D
Refer the attached figure below.
Earth has a radius of 6371 kilometers
i.e, CB=CD=6371 km
Total distance CA=CD+DA=6371+6.6=6377.6
The pilot's distance to the horizon is A.
Using Pythagorean theorem,
[tex]CA^2=AB^2+CB^2[/tex]
[tex]6377.6^2=AB^2+6371^2[/tex]
[tex]AB=\sqrt{40673781.76-40589641}[/tex]
[tex]AB=\sqrt{84140.76}[/tex]
[tex]AB=290.07[/tex]
Rounded to the nearest tenth, AB=290.1 km
So, the pilot's distance to the horizon is 290.1 kilometers.
