Question

question 32 (1 point)
the central angle subtended by an arc of 5.4 cm is 51.5°. the radius of the circle, to the nearest hundredth, is

Explanation:

Step1: Convert angle to radians

First, convert $51.5^{\circ}$ to radians. We know that $1^{\circ}=\frac{\pi}{180}$ radians. So, $\theta = 51.5\times\frac{\pi}{180}\text{ radians}\approx0.90\text{ radians}$.

Step2: Use arc - length formula

The arc - length formula is $s = r\theta$, where $s$ is the arc - length, $r$ is the radius and $\theta$ is the central angle in radians. We are given $s = 5.4$ cm and $\theta\approx0.90$ radians. Rearranging the formula for $r$, we get $r=\frac{s}{\theta}$.

Step3: Calculate the radius

Substitute $s = 5.4$ cm and $\theta\approx0.90$ radians into the formula $r=\frac{s}{\theta}$. So, $r=\frac{5.4}{0.90}=6.00$ cm.

Answer:

$6.00$ cm