# Pilot

How high is the airplane's pilot to see 0.001 of Earth's surface?

Result

h =  12.782 km

#### Solution:

$R = 6378 \ km \ \\ S_{ 1 } = 4 \pi \cdot \ R^2 = 4 \cdot \ 3.1416 \cdot \ 6378^2 \doteq 511185932.5225 \ km^2 \ \\ S = 0.001 \cdot \ S_{ 1 } = 0.001 \cdot \ 511185932.5225 \doteq 511185.9325 \ km^2 \ \\ \ \\ S = 2 \pi R v \ \\ v = S / (2 \pi \cdot \ R) = 511185.9325 / (2 \cdot \ 3.1416 \cdot \ 6378) = \dfrac{ 3189 }{ 250 } = 12.756 \ km \ \\ y = R - v = 6378 - 12.756 = 6365.244 \ km \ \\ x = \sqrt{ R^2-y^2 } = \sqrt{ 6378^2-6365.244^2 } \doteq 403.1784 \ km \ \\ \ \\ x/y = (h+v)/x \ \\ h+v = x^2/y \ \\ h = x^2/y - v = 403.1784^2/6365.244 - 12.756 = \dfrac{ 6378 }{ 499 } \doteq 12.7816 = 12.782 \ \text{ km }$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.

## Next similar math problems:

1. Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
2. 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.
3. Spherical cap 4
What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
4. Thunderstorm
The height of the pole before the storm is 10 m. After a storm when they come to check it they see that on the ground from the pole blows part of the column. Distance from the pole is 3 meters. At how high was the pole broken? (In fact, a rectangular tria
5. Depth angles
At the top of the mountain stands a castle, which has a tower 30 meters high. We see the crossroad in the valley from the top of the tower and heel at depth angles of 32° 50 'and 30° 10'. How high is the top of the mountain above the crossroad
6. Spherical cap
What is the surface area of a spherical cap, the base diameter 20 m, height 2 m.
Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
8. Calculate
Calculate the length of a side of the equilateral triangle with an area of 50cm2.
9. If the
If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
10. Isosceles trapezium
Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
11. Equilateral triangle
The equilateral triangle has a 23 cm long side. Calculate its content area.
12. The ditch
Ditch with cross section of an isosceles trapezoid with bases 2m 6m are deep 1.5m. How long is the slope of the ditch?
13. Median in right triangle
In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
14. Hypotenuse
Calculate the length of the hypotenuse of a right triangle if the length of one leg is 4 cm and its content area is 16 square centimeters.
15. A truck
A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
16. Triangle
Calculate the area of right triangle ΔABC, if one leg is long 14 and its opposite angle is 59°.
17. Triangle P2
Can triangle have two right angles?