what is the height of the earth's atmosphere?

The Earth's atmosphere doesn't really stop at a certain place and then "space" begins. The air gets thinner as you go up from the surface and the higher the altitude, the thinner it is until you reach interplanetary space. It gets thinner still if you leave our solar system. But it is always there.

In reality, no volume of space can ever be perfectly empty. A perfect vacuum with a gaseous pressure of absolute zero is a philosophical concept that does not exist in nature.

Nevertheless, several boundaries have been designated:

~ The Fédération Aéronautique Internationale has established the Kármán line at an altitude of 100 kilometers (62 mi) as a working definition for the boundary between aeronautics and astronautics. This is used because above that altitude, as Theodore von Kármán calculated, a vehicle would have to travel faster than orbital velocity in order to derive sufficient aerodynamic lift from the atmosphere to support itself.

~ The United States designates people who travel above an altitude of 50 miles (80 km) as astronauts.

~ NASA's mission control uses 76 miles (122 km) as their re-entry altitude, which roughly marks the boundary where atmospheric drag becomes noticeable, (depending on the ballistic coefficient of the vehicle), thus leading shuttles to switch from steering with thrusters to maneuvering with air surfaces.

A space ship could orbit the Earth at any altitude from the mountain tops out to about 1.5 million kilometers (932,000 miles) at the limit of the "Hill Sphere".

At the mountain tops, the atmospheric drag would cause the orbit to decay very quickly.

The outer limit of the Hill Sphere is the distance where the Sun's gravity would pull it out of orbit.

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There is no technical boundary, but the effects would start being felt by a spaceship around 120 km from the surface.

once you have the answers what will you do with the information