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


x =  22.02 m


S1+S2=12S S=πr2 S1=12x2(αsinα) S2=12r2((2π2α)sin(2π2α))  x=2rcos(α/2)   α=tanαπ2cosα    x=1.158728419=22.02 mS_1 + S_2 = \dfrac12 S \ \\ S = \pi r^2 \ \\ S_1 = \dfrac12x^2(\alpha -\sin \alpha) \ \\ S_2 = \dfrac12r^2((2\pi - 2\alpha) -\sin (2\pi - 2\alpha)) \ \\ \ \\ x = 2r \cos (\alpha/2) \ \\ \ \\ \ \\ \alpha = \tan \alpha - \dfrac{ \pi }{ 2 \cos \alpha } \ \\ \ \\ \ \\ \ \\ x = 1.1587284 \cdot 19 = 22.02 \ \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!

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

Showing 0 comments:
1st comment
Be the first to comment!

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



Next similar math problems:

  1. Hexagon A
    hexagon Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
  2. Chord - TS v2
    chord_TS_1 The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
  3. Cable
    wire Cable consists of 8 strands, each strand consists of 12 wires with diameter d = 0.5 mm. Calculate the cross-section of the cable.
  4. 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.
  5. RT and circles
    r_triangle Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
  6. Triangle
    star Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
  7. Balls
    stats We have n identical balls (numbered 1-n) is selected without replacement. Determine 1) The probability that at least one tensile strength number coincides with the number of balls? 2) Determine the mean and variance of the number of balls, which coincides
  8. Height 2
    1unilateral_triangle Calculate the height of the equilateral triangle with side 38.
  9. Two triangles SSA
    ssa Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
  10. SAS triangle
    triangles2 The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle.
  11. Theorem prove
    thales_1 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?
  12. Unknown number
    mocninova_fx I think number. If subtract from the twelfth square the ninth square I get a number 27 times greater than the intended number. What is this unknown number?
  13. Sails
    ship_nina We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
  14. Asymptote
    asymptote What is the vertical asymptote of ?
  15. Trigonometry
    sinus Is true equality? ?
  16. Inverse matrix
    matrix_3 Find how many times is the larger determinant is the matrix A, which equals 9 as the determinant of its inverse matrix.
  17. The determinant
    matrix_13 The determinant of the unit matrix equals 7. Check how many rows the A matrix contains.