Find the radius of a circle in which the central angle, a, intercepts an arc of the given length s. a = 156°, s = 25 km

Radius of the circle is 9.178

Step-by-step explanation:

Given that,

Central angle, a = 156°

Arc length, s = 25 km

The formula to calculate the radius of a circle is;

Arc length = Θ / 360° x (2πr)

We are given that the Θ = 20° and that arc length is 66 in. Substituting, we have;

L = Θ / 360° x (2πr)

25 = (156 / 360°) x 2 x 22/7 x r

25 = 6864r / 2520

r = (2520 x 25) / 6864

r = 63000 / 6864

r = 9.178