Find the radius of a circular sector with an arc length 26 feet and a central angle $\frac { 3 \pi } { 2 }$ radians. Round your answer to two decimal places.
A) $5.52 \mathrm { feet }$
B) $12.41$ feet
C) $3.40$ feet
D) $0.18$ foot
E) $0.08$ foot

Question

Quizplus · Accepted Answer

The formula to find the radius $r$ of a circular sector given the arc length $L$ and the central angle in radians $\theta$ is $L = r\theta$. Plugging in the given values, $26 = r\left(\frac{3\pi}{2}\right)$. Solving for $r$ gives $r = \frac{26}{\frac{3\pi}{2}} = \frac{26 \times 2}{3\pi} \approx 5.52$ feet.

Find the Radius of a Circular Sector with an Arc 3π2\frac { 3 \pi } { 2 }23π​

Find the Radius of a Circular Sector with an Arc $\frac { 3 \pi } { 2 }$