The length of the arc is a fraction of the circumference of the circle depending on the length of the radius and the intercepted angle. This can be calculated through the equation,
L = (2πr) x (θ /360)
where L is the length of arc, r is the radius, and θ is the intercepted angle in terms of degrees.
Substituting the known values to the equation,
36 = (2π)(15) x (θ / 360)
We translate the equation to find the value of θ,
θ = (36)(360) / 2π(15)
The value of θ is equal to 137.51°.
This can be coverted to radians through the equation below,
θ (in radians) = 137.51° x (2π rad / 360°) = 2.4 rad
