Question

In a circle with a diameter of 25.2 ft. An arc is intercepted by a central angle of 168°. What is the arch length? Use 3.14 for pi and round your final answer to the nearest hundredth.

Answer 1

if the circle has a diameter of 25.2, its radius is half that or 12.6.

`\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=12.6\\ \theta =168 \end{cases}\implies s=\cfrac{\pi (168)(12.6)}{180} \\\\\\ s=11.76\pi \implies \implies \stackrel{\pi =3.14~\hfill }{s=36.9264}\implies \stackrel{\textit{rounded up}}{s=36.93}`