Airplane

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

Correct result:

h =  4.9947 km

Solution:

R=6378 km S=200000 km2  S=2πRv v=S/(2π⋅ R)=200000/(2⋅ 3.1416⋅ 6378)≐4.9907 km y=R−v=6378−4.9907≐6373.0093 km x=R2−y2=63782−6373.00932≐252.2639 km k=\cotanα=x/y=(h+v)/x x/y=(h+v)/x h+v=x2/y h=x2/y−v=252.26392/6373.0093−4.9907=4.9947 km

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