Question

If a door that is 36 inches in width opens to an angle of 140 , what is the length of the arc created by the door?

Answer 1

So hmm check the picture below

$\bf s=\cfrac{r\pi \theta}{180}\qquad \begin{cases} s=\textit{length of the arc}\\ \theta=\textit{central angle in degrees}\\ r=radius\\ ----------\\ r=36\\ \theta=140 \end{cases}\implies s=\cfrac{36\cdot \pi \cdot 140}{180}$