Question

Earth has a radius of 6371 kilometers. A pilot is flying at a steady altitude of 6.6 kilometers above the earth's surface.

Answer 1

Check the picture below.

Answer 2

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,

$CA^2=AB^2+CB^2$

$6377.6^2=AB^2+6371^2$

$AB=\sqrt{40673781.76-40589641}$

$AB=\sqrt{84140.76}$

$AB=290.07$

Rounded to the nearest tenth, AB=290.1 km

So, the pilot's distance to the horizon is 290.1 kilometers.