Answer:
[tex]\frac{\beta }{2\pi } *2\pi r\\[/tex]
Step-by-step explanation:
We know that perimeter of a circle is given by 2πr (where r is the radius of the circle).
We can say that for an complete angle of 2π the perimeter is 2πr.
Now let us consider a small section of segment making an angle β at the centre.
According to the proportionality rules the length of the small segment would be
[tex]\frac{\beta }{2\pi } *2\pi r\\[/tex]
Let the perimeter of circle be P then
[tex]\frac{\beta }{2\pi } *P[/tex]
Hence this is the formula for length of an arc subtending angle β.
