Cartoons of cool ideas

from science and mathematics

View from a Plane View from a Plane

Have you wondered how far away you can see if you are in an airplane at 30,000 feet above ground? If there are no clouds or anything blocking the view, you can see approximately 200 miles away (along the ground). Because Earth is round, any distance further than that is out of view (unless there are particularly tall mountains on the horizon).

You can compute how far the horizon is using only high school trigonometry! The triangle formed by the airplane, the center of Earth, and the furthest visible point on land form a right triangle. After looking up the radius of Earth, you can then compute the angles of this triangle and the length of the circular arc along Earth that corresponds to your view. You will get an answer around 200 miles.