# Moon

We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.

Result

x =  425520 km

#### Solution:

$r=1740 \ \text{km} \ \\ u=28/60=\dfrac{ 7 }{ 15 } \doteq 0.4667 \ ^\circ \ \\ \ \\ v=u/2=0.4667/2 \doteq \dfrac{ 7 }{ 30 } \doteq 0.2333 \ ^\circ \ \\ \ \\ w=\dfrac{ \pi }{ 180 } \cdot \ v=\dfrac{ 3.1416 }{ 180 } \cdot \ 0.2333 \doteq 0.0041 \ \text{rad} \ \\ \ \\ \tan(w)=r/(x+r) \ \\ \ \\ x=r/\tan(w)-r=1740/\tan(0.0041)-1740 \doteq 425520.4509 \doteq 425520 \ \text{km}$

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
Do you want to convert length units?

## Next similar math problems:

1. Chord MN
Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle.
2. Equilateral triangle
How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it?
3. Right triangle
Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.
4. High wall
I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall?
5. Cable car
Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
6. Maple
Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
7. Flowerbed
Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
8. Tree
How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground.
9. Building
The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
10. 30-60-90
The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
11. Reflector
Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
12. The Eiffel Tower
The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height.
13. The cable car
The cable car has a length of 3,5 kilometers and an angle of climb of 30 degrees. What is the altitude difference between Upper and Lower Station?
14. Isosceles triangle 10
In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.
15. Height 2
Calculate the height of the equilateral triangle with side 38.
16. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
17. Center traverse
It is true that the middle traverse bisects the triangle?