Question

Earth has a radius of 6371 kilometers. A pilot is flying at a steady altitude of 5.6 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

As the Earth has a radius of 6371 kilometers and pilot is flying at a steady altitude of 5.6 kilometers above the earth's surface. This forms a right angled triangle of perendicular 6371km and hypotenuse of (6371+5.6)km. The pilot's distance to the horizon will be the Base.Hence by pythagoras theorem we have Distance=276.5km rounding of =280km

Answer 2

The pilot's distance to the horizon is 267.2 kilometers.

Explanation:

According to the below diagram,
`A` is the position of the pilot which is 5.6 kilometers above the earth's surface,
`D`.

Earth has a radius of 6371 kilometers. That means,
`CB=CD= 6371` kilometers.

So,
`CA= CD+DA= (6371+5.6)= 6376.6` kilometers.

The pilot's distance to the horizon is
`AB`.

Using Pythagorean theorem, we will get........

`AB^2+CB^2 = CA^2\\ \\ AB^2+(6371)^2=(6376.6)^2\\ \\ AB^2 = (6376.6)^2 -(6371)^2 \\ \\ AB^2= 71386.56\\ \\ AB= √(71386.56)=267.182... \approx 267.2`

(Rounded to the nearest tenth)

So, the pilot's distance to the horizon is 267.2 kilometers.