Question

b) what is the angle in radians when the radius = 12 cm and the intercepted arc = 16π cm?

Explanation:

Step1: Recall the formula for arc length

The formula for arc length \(s\) is \(s = r\theta\), where \(r\) is the radius and \(\theta\) is the angle in radians.

Step2: Solve for \(\theta\)

Given \(s = 16\pi\) cm and \(r = 12\) cm. Rearranging the formula \(\theta=\frac{s}{r}\), we substitute the values: \(\theta=\frac{16\pi}{12}\).

Step3: Simplify the fraction

\(\theta=\frac{4\pi}{3}\) radians.

Answer:

\(\frac{4\pi}{3}\) radians