How To Calculate The Length Of The Arc | The Science



The Science

How to calculate the length of the arc

Arc of a circle is a part of a circle included between two of its points. It can be described as ASB, where A and B - the ends. The length of the arc can be expressed in terms of contracting chord, radius of the circle and the angle between the radius drawn to the ends of the chord.

How to calculate the length of the arc

Instruction how to calculate the length of the arc

Step 1:

Let ACB - arc, R - its radius, O - the center of the circle. The segments OB and OC will be the radius of the circle. Let the angle between them is equal to?. Then ACB = R ?, where the angle? expressed in radians - the arc length okruzhnosti.Esli angle? expressed in degrees, the circumferential length of the arc equals: ACB = R * pi * / 180?.

Step 2:

The chord AB subtends arc ASB. Let the known length of the chord AB and the angle? between the radii OA and OB. AOB triangle - isosceles, since OA = OB = R.

Step 3:

The height of the OE in the triangle AOB is also its bisector and median. Consequently, the angle AOE = AOB / 2 =? / 2, and AE = BE = AB / 2. Consider AEO triangle. Since OE - height, it is a square (corner of AOE - direct). AO - its hypotenuse, and AE - his leg. Hence, R = OA = (AB / 2) / sin (? / 2). Consequently, ACB = (AB / 2) / sin (? / 2) * pi *? / 180