Use this formula and solve for the radius 'r'.The chord length formula is, 2r sin (θ/2).Step 3: Arc length = rθ = 5 × 2 = 10 units.By taking square root on both sides, r = 5. Then find the arc length using the relevant formula.Įxample: Calculate the arc length of a curve with sector area 25 square units and the central angle as 2 radians.We need to use the square root in this process. The sector area formula is, (θ/360º) × πr 2, if θ is in degrees (or) (1/2) r 2θ, if θ is in radians.The arc length of a circle can be calculated without the radius using: How to Find Arc Length Without the Radius? Length of an Arc = θ × (π/180) × r, where θ is in degree.Length of an Arc = θ × r, where θ is in radian.The arc length of a circle can be calculated with the radius and central angle using the arc length formula, How to Find Arc Length With the Radius and Central Angle? find arc length without the central angle.find arc length with the radius and central angle.The arc length of an arc of a circle can be calculated using different methods and formulas based on the given data. The arc length formula in radians can be expressed as, The arc length of a circle can be calculated using different formulas, based on the unit of the center angle of the arc. The arc length formula can be expressed as:Īrc length, L = θ × r, when θ is in radian Īrc length, L = θ × (π/180) × r, where θ is in degrees, Thus, the arc of a circle formula is θ times the radius of a circle, if the angle is in radians. By substituting this in the above formula, If θ is in radians, then the angle in degrees = θ × 180/π. The measurements of the central angle can be given in degrees or radians, and accordingly, we calculate the arc length of a circle. The length of an arc can be calculated using different formulas, based on the unit of the central angle of the arc. This is the arc length formula when the angle is in degrees. If the angle subtended by an arc is θ°, then it means that the arc occupies a fraction of θ/360 out of the total circumference. We know that the angle at the center in a full circle is 360°. But arc is just a part (in fact a fraction) of the total circumference. To derive the arc length formula, let us recall what is the circumference of a full circle whose radius is 'r'.
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