Earth's circumference

Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.

Correct answer:

x =  26728.1018 km

Step-by-step explanation:

$$\begin{gathered} R=6378\text{ km } \\ \alpha =48{\displaystyle \frac{10}{60}}={\displaystyle \frac{48\cdot 60+10}{60}}={\displaystyle \frac{2890}{60}}={\displaystyle \frac{289}{6}}\doteq 48.1667^{\circ } \\ \cos \alpha =r\mathrm{/}R \\ r=R\cdot \cos {\alpha }^{\circ }=R\cdot \cos 48.166666666667^{\circ }=6378\cdot \cos 48.166666666667^{\circ }=6378\cdot 0.666966=4253.90952\text{ km } \\ x=2\pi \cdot r=2\cdot 3.1416\cdot 4253.9095=26728.1018\text{ km}=2.673\cdot 10^4\text{ km} \end{gathered}$$

Try another example

Related math problems and questions:

• Earth parallel
  Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°.
• Rotation of the Earth
  Calculate the circumferential speed of the Earth's surface at a latitude of 61°​​. Consider a globe with a radius of 6378 km.
• The spacecraft
  The spacecraft spotted a radar device at altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered a
• What percentage
  What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km
• Felix
  Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km.
• 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.
• Triangle in circle
  Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
• Chimney
  The lower circumference of the chimney is 12.57 m, and the top circumference is 5.655 m. The slope of the walls is 87°. Find the height of the chimney.
• Elevation
  What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
• The hemisphere
  The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
• Chord - TS
  The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS?
• Cosine
  Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
• The mast
  A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
• Horizon
  The top of a lighthouse is 19 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
• 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'.
• The Earth
  The Earth's surface is 510,000,000 km². Calculates the radius, equator length, and volume of the Earth, assuming the Earth has the shape of a sphere.
• Right triangle
  It is given a right triangle angle alpha of 90 degrees beta angle of 55 degrees c = 10 cm use Pythagorean theorem to calculate sides a and b