How Far Can You See from a Plane?

The video explores how far one can see from a plane at a cruising altitude of 10 km. Assuming Earth is a perfect sphere with a radius of 6,371 km, the problem is solved using the Pythagorean theorem. The calculation shows that on a clear day, visibility extends approximately 357 km in any direction from the plane. This is illustrated with a map of North America, highlighting the significant area visible from such an altitude.

What is the cruising altitude of the plane used in this problem?

• 20 kilometers

• 5 kilometers

• 10 kilometers

• 15 kilometers

What assumption is made about the shape of Earth in this problem?

• Earth is a perfect sphere

• Earth is a perfect cube

• Earth is a flat surface

• Earth is a perfect cylinder

What is the radius of Earth assumed to be in this problem?

• 8,000 kilometers

• 7,000 kilometers

• 6,371 kilometers

• 5,000 kilometers

In the geometric setup, what does the line of sight from the plane form with Earth's surface?

• A tangent

• A diagonal line

• A parallel line

• A perpendicular line

What mathematical theorem is used to calculate the distance one can see from the plane?

• Fundamental theorem of calculus

• Binomial theorem

• Fermat's Last Theorem

• Pythagorean theorem

What is the length of the hypotenuse in the right triangle used in the calculation?

• 6,371 kilometers

• 6,381 kilometers

• 6,391 kilometers

• 6,401 kilometers

What is the approximate distance one can see from the plane on a clear day?

• 357 kilometers

• 457 kilometers

• 257 kilometers

• 157 kilometers

What is the significance of the tangent line in this problem?

• It is parallel to the radius

• It is perpendicular to the radius

• It is diagonal to the radius

• It is equal to the radius

How does the calculated distance relate to viewing a map of North America?

• It covers a small city

• It covers an entire state

• It covers a continent

• It covers a country

What is the altitude of 10 kilometers approximately equal to in feet?

• 32,000 feet

• 20,000 feet

• 10,000 feet

• 40,000 feet