Question

Find the radian measure of angle theta, if theta is a central angle in a circle of radius 4, and theta cuts off an arc of length 16

Answer 1

The relationship between the length, L, of an arc of a circle (of radius r) cut off by a central angle theta (measured in radians) is given as:

$L=r\theta$

Given that:

$L=16\text{ and r = 4}$

we have that:

$\begin{gathered} 16=(4)\theta \\ \frac{16}{4}=\theta \\ 4=\theta \\ \Rightarrow\theta=4\text{ radians} \end{gathered}$