Airplane

Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?

Correct answer:

h =  4.9947 km

Step-by-step explanation:

$$\begin{gathered} R=6378\text{ km } \\ S=200000{\text{km}}^2 \\ S=2\pi Rv \\ v=S\mathrm{/}(2\pi \cdot R)=200000\mathrm{/}(2\cdot 3.1416\cdot 6378)\doteq 4.9907\text{ km } \\ y=R-v=6378-4.9907\doteq 6373.0093\text{ km } \\ x=\sqrt{R^2-y^2}=\sqrt{6378^2-6373.0093^2}\doteq 252.2639\text{ km } \\ k=\text{cotan}\alpha =x\mathrm{/}y=(h+v)\mathrm{/}x \\ x\mathrm{/}y=(h+v)\mathrm{/}x \\ h+v=x^2\mathrm{/}y \\ h=x^2\mathrm{/}y-v=252.2639^2\mathrm{/}6373.0093-4.9907=4.9947\text{ km} \end{gathered}$$

Try another example

Related math problems and questions:

• Pilot
  How high is the airplane's pilot to see 0.001 of Earth's surface?
• Spherical cap
  Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm². Determine the radius r of the sphere from which the spherical cap was cut.
• Above Earth
  To what height must a boy be raised above the earth to see one-fifth of its surface.
• Spherical cap 4
  What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
• Spherical cap
  From the sphere of radius 11 was truncated spherical cap. Its height is 6. What part of the volume is a spherical cap from the whole sphere?
• Spherical cap
  What is the surface area of a spherical cap, the base diameter 20 m, height 2 m.
• Sphere - parts
  Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm.
• Spherical cap
  The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut.
• The Earth
  The Earth's surface is 510,000,000 km². Calculates the radius, equator length, and volume of the Earth, assuming the Earth has the shape of a sphere.
• Elevation
  What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
• Cube and sphere
  Cube with the surface area 150 cm² is described sphere. What is sphere surface?
• Sphere parts, segment
  A sphere with a diameter of 20.6 cm, the cut is a circle with a diameter of 16.2 cm. .What are the volume of the segment and the surface of the segment?
• A spherical segment
  A spherical section whose axial section has an angle of j = 120° in the center of the sphere is part of a sphere with a radius r = 10 cm. Calculate the cut surface.
• Tropics and polar zones
  What percentage of the Earth's surface lies in the tropical, temperate, and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33'.
• Spherical segment
  The spherical segment with height h=1 has a volume V=223. Calculate the radius of the sphere of which is cut this segment.
• An observer
  An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
• Two hemispheres
  In a wooden hemisphere with a radius r = 1, a hemispherical depression with a radius r/2 was created so that the bases of both hemispheres lie in the same plane. What is the surface of the created body (including the surface of the depression)?