arc length formula

The arc length for a sector of a circle is given by the arc length formula S = r.θ

Here S - represents the arc length - represents the radius of the circle θ - represents the angle in radians made by the arc at the centre of the circle The application of the arc length formula can be better understood with an example Find the length of the arc using the Arc length formula which subtends an angle of 60 degrees at the centre of a circle whose radius is 5 cms. Step1: The angle subtended by the arc is given in degrees. So need to convert the angle in to radians using a simple formula. π radians = 180 degrees Divide both sides by 3 π/3 radians = 180/3 = 60 degrees

Now we have the radian measure of the angle as pi/3, the radius is given as 5 cms, apply the arc length formula S = r.π

S = 5 . π/3

We know the value of &pi is 3.14 (approx) but to get a more precise value key in the computation using your graphic calculator.

So arc length S is given by 5 . π/3 = 5.2359 cms

Note: The radian measure of an angle is used instead of the degree measure to simplify the arc length formula.