Please give me the answer for this problem ...................?

Question

A circular park of radius 20m is situated in a colony. Three boys A,B and C are sitting at equal distance on its boundry each having a toy telephone in their hand to talk to each other.find the length of the string of each phone.

many of you have given me the length of the arcs.but thats not what I need. I need the length of the strings that they are holding i,e.,,when you draw a figure,it appears as an equilateral triangle in a circle .I want the length of each side of the triangle.

Answer 1

cirumference is 2rpi so it is 40pi or approximately 125.6637 then divide by three because people are all equally spaced so the final answer is 41.88 or about 42m.
But because lstrings do not form chords when streched but, only straight lines you will have in equaliteral triangle which you now because a one chord is equal to 2pi/3 forming a vertex angle thus angle =2pi/3 ,convert radians to degree that is 60. Then because of Relations beteen polar and retangular coordinates the y coordinate is equal to (sin60)2r thus answer is 34.6410161514

Answer 2

34.641 is the correct answer. Draw the triangle inside the circle. Now draw a line from the center of the circle to one vertex of the triangle, and draw a perpendicular to one side of the triangle, forming a right triangle. Since all the angles at the center of the circle are 360 degrees, the angles between radii joining the center to the vertices is 120 degrees, and divide by 2 to find the angle between the perpendicular and the radius.
Now the triangle is a 30-60-90 right triangle. The hypotenuse is 20 and the leg opposite the 30 degree angle is 10. Use the Pythagorean theorem to find the other leg (sqrt 300, or 17.32. Double this to find the lengths of the sides of the triangle.

Answer 3

U have Given Radius As 20 mts.Then the Circumference is 2 * PI * R i.e


2 * 22/7 * 20 that will give u 125.714

The three persons are sitting on the circumference with equidistance from each other. then u should divede circumference by 3 to get the distance between them.

i.e

125.714/3

41.91
which is apprximately equal to 42 meters.

Answer 4

if the string is straight between any two boys then the length of string =20 / sine(120) = 34.4464601m
if the string is cricular along the boundry then the length of
string =(40 * pi) / 3 = 41.887902

Answer 5

I am not sure, but this is how i worked it out.

Circumference of a circle = 2 pi r
= 22/7 * 2 * 20
= 125.714 m

Length of each string = 125.714/3 = 42 m

Answer 6

Length of each string = 2 *20sin60°
= 20√3m
≈ 34.641m

Answer 7

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Answer 8

If they are can-and-string phones, and each boy has only one can then each phone string is 20 m, the distance to the center, plus a little for knots.

Answer 9

the length of
string =(40 * pi) / 3 = 41.887902

Answer 10

the length=2pir/3
=2*3.14*20/3
=41.87 m
however if they are holdingit in a straight line it will be equalto the length of the chord
=2rsin60*
=2*20*rt3/2
=34.6 m