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?

Answer 1

The pilot's distance to the horizon is 267.2 km

Answer 2

The pilot's distance to the horizon is 267.183 kilometers.

Explanation:

It is given that earth has a radius of 6371 kilometers. A pilot is flying at a steady altitude of 5.6 kilometers above the earth's surface.

Using Pythagoras theorem in triangle OAB, we get

`OA^2=OB^2+AB^2`

`(6371+5.6)^2=(6371)^2+AB^2`

`40661027.56-40589641=AB^2`

`71386.56=AB^2`

Taking square root on both the sides,

`√(71386.56)=AB`

`267.182634166=AB`

`267.183\approx AB`

Therefore the pilot's distance to the horizon is 267.183 kilometers.