Question

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

Answer 1

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

Answer 2

Answer:

$75\°$

Step-by-step explanation:

we know that

The circumference of a circle is equal to

$C=2\pi r$

In this problem we have

$r=6\ m$

substitute the value

$C=2\pi (6)=12\pi\ m$

Remember that

$360\°$ subtends the complete circle of length arc $12\pi\ m$

so

by proportion

Find the central angle for an arc length of $\frac{5\pi}{2}\ m$

$\frac{360}{12\pi}\frac{degrees}{m}=\frac{x}{\frac{5\pi}{2}}\frac{degrees}{m} \\ \\ x=(5/2)*360/12\\ \\x=75\°$