Question

Hello, how are you? I would like you to help me solve this exercise, please!

Answer 1

Given

Formula for the length of an arc

$\begin{gathered} Measureof\text{Arc of a circle=}\frac{\theta}{360}\times2\pi r \\ \\ \end{gathered}$

Parameters;

$\begin{gathered} \theta=?\text{ , r=1m} \\ \text{measure of arc =}\frac{\pi}{9} \end{gathered}$

We can substitute into the formula

$\begin{gathered} \frac{\pi}{9}=\frac{\theta}{360}\times2\times\pi\times1 \\ \\ \frac{\pi}{9}=\frac{2\theta\pi}{360} \\ \text{cross multiply} \\ 18\theta\pi=360\pi \\ divide\text{ both sides by 18}\pi \\ \frac{18\theta\pi}{18\pi}=\frac{360\pi}{18\pi} \\ \theta=20^0 \end{gathered}$

Now, change to radian

$\frac{\pi}{180}\times20^0=\frac{20^0\pi}{180^0}=\frac{\pi}{9}$

The final answer

$\frac{\pi}{9}$