MATH SOLVE

4 months ago

Q:
# for a circle with a radius of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with a length of 5/2 pi meters

Accepted Solution

A:

[tex]\bf \textit{arc's length}\\\\
s=\cfrac{\pi r\theta }{180}\quad
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=6\\
s=\frac{5\pi }{2}
\end{cases}\implies \cfrac{5\pi }{2}=\cfrac{\pi \cdot 6\cdot \theta }{180}\implies \cfrac{5\pi }{2}=\cfrac{\pi \theta }{30}
\\\\\\
\cfrac{5\underline{\pi }\cdot 30}{2\underline{\pi} }=\theta \implies 75=\theta[/tex]