# Airplane

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

Result

h =  4.995 km

#### Solution:

$R = 6378 \ km \ \\ S = 200000 \ km^2 \ \\ \ \\ S = 2 \pi R v \ \\ v = S / (2 \pi \cdot \ R) = 200000 / (2 \cdot \ 3.1416 \cdot \ 6378) \doteq 4.9907 \ km \ \\ y = R - v = 6378 - 4.9907 \doteq 6373.0093 \ km \ \\ x = \sqrt{ R^2-y^2 } = \sqrt{ 6378^2-6373.0093^2 } \doteq 252.2639 \ km \ \\ k = \cotan \alpha = x/y = (h+v)/x \ \\ x/y = (h+v)/x \ \\ h+v = x^2/y \ \\ h = x^2/y - v = 252.2639^2/6373.0093 - 4.9907 \doteq 4.9947 = 4.995 \ \text { km }$

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#### Following knowledge from mathematics are needed to solve this word math problem:

Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

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