Question

If theta equals 120° what is the measure of arc AD in radians?

Answer 1

To calculate the length of an arc we can apply the following expression:

`l\text{ = 2}\cdot\pi\cdot r(\theta)/(360)`

Where l is the length of the arc, r is the radius and theta is the angle of the arc. This is an unitary circle, which means that its radius is equal to 1. With this information we can calculate the length of the arc:

`\begin{gathered} l=2\cdot\pi\cdot1\cdot(120)/(360) \\ l=(2)/(3)\cdot\pi \end{gathered}`

The lenth of the arc is equal to 2/3 pi radians.