Goat

Meadow is a circle with a radius r = 19 m. How long must a rope tie a goat to the pin on the perimeter of the meadow to allow the goat to eat half of the meadow?

Correct answer:

x =  22.02 m

Step-by-step explanation:

S1+S2=12S S=πr2 S1=12x2(αsinα) S2=12r2((2π2α)sin(2π2α))  x=2rcos(α/2)   α=tanαπ2cosα    x=1.158728419=22.02 m



Did you find an error or inaccuracy? Feel free to write us. Thank you!



avatar







Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our right triangle calculator.
See also our trigonometric triangle calculator.

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

Related math problems and questions:

  • Goat and circles
    equation_nonlinear What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g
  • Equilateral triangle
    3angle_in_circle How long should the minimum radius of the circular plate be cut an equilateral triangle with side 19 cm from it?
  • Triangle
    star Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
  • SAS triangle
    triangles2 The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle.
  • Decagon
    decanon Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
  • An equilateral
    goat__wolf_and_cabbage An equilateral triangle with a side of 10 m represents a wooden platform standing on a lawn. A goat is tied to a corner with a 15 m rope. What is the maximum amount of grazing area available to the goat?
  • Rectangle field
    land The field has a shape of a rectangle having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m?
  • Pentagon
    5gon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
  • Goat
    hexagon The fenced flower bed has the shape of a regular hexagon. The tops are formed by fence posts. The fence around the flowerbed measures 60 m. A goat is tied to one of the pillars from the outside and grazes on the surrounding meadow (the goat should not ent
  • Right triangle eq2
    rt_triangle Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
  • Diagonals of pentagon
    5gon_diagonal Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
  • 30-gon
    30gon At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
  • Trapezoid MO
    right_trapezium The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
  • Triangle SAA
    triangle_blue The triangle has one side long 71 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
  • Triangle in circle
    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.
  • Hexagon A
    hexagon Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
  • Horses playground
    kone_dzokej The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m2, the base lengths should be 31 m and 19 m. How many meters of boards will they need to fence it if the boards are stacked in 5 rows?