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.

What is the pilot's distance to the horizon?

Enter your answer, rounded to the nearest tenth, in the box.

Answer 1

check the picture below.

Answer 2

The pilot's distance to the horizon is 290.1 kilometers.

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=√(40673781.76-40589641)`

`AB=√(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.