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.

Correct result:

h =  22482.4 m

Solution:

R=6378.1 km d=536 km  (R+h)2=d2+R2 R+h=d2+R2 h=d2+R2R h=5362+6378.126378.1 h=22482.4 mR = 6378.1 \ km \ \\ d = 536 \ km \ \\ \ \\ (R+h)^2 = d^2 + R^2 \ \\ R+h = \sqrt{ d^2 + R^2 } \ \\ h = \sqrt{ d^2 + R^2 } - R \ \\ h = \sqrt{ 536^2 + 6378.1^2 } - 6378.1 \ \\ h = 22482.4 \ \text{m}



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!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Next similar math problems:

  • Sphere cuts
    sphere_cut At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.
  • Double ladder
    rr_rebrik The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
  • Common chord
    chord2 Two circles with radius 17 cm and 20 cm are intersect at two points. Its common chord is long 27 cm. What is the distance of the centers of these circles?
  • The double ladder
    dvojity_rebrik The double ladder has 3 meters long shoulders. What is the height of the upper of the ladder reach if the lower ends are 1.8 meters apart?
  • Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  • Double ladder
    dvojak The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
  • Horizon
    lighthouse 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.]
  • Circumscribing
    thales Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
  • RT - inscribed circle
    rt_incircle In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
  • Distance
    origin_math Wha is the distance between the origin and the point (18; 22)?
  • Two parallel chords
    chords_equall The two parallel chords of the circle have the same length of 6 cm and are 8 cm apart. Calculate the radius of the circle.
  • Is right triangle
    triangle_1111_4 Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m
  • Isosceles IV
    iso_triangle In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
  • Stairway
    schody Stairway has 20 steps. Each step has a length of 22 cm and a height of 15 cm. Calculate the length of the handrail of staircases if on the top and bottom exceeds 10 cm.
  • Euclid 5
    euclid_3 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
  • The ladder
    rebrik The ladder has a length of 3 m and is leaning against the wall, and its inclination to the wall is 45°. How high does it reach?
  • Thales
    circles_1 Calculate the length of the Thales' circle described to right triangle with hypotenuse 44.2 cm.