Question

Given a central angle of q = 75° and a radius 6 inches, calculate the length of a chord connecting the endpoints of the two radii that make up the central angle.

Answer 1

check the picture below.


`\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ \theta =75\\ r=6 \end{cases}\implies s=\cfrac{(\pi )(75)(6)}{180}\implies s=\cfrac{5\pi }{2}`