Question

the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°. what is the approximate length of the radius of the circle? a. 10.38 units b. 11.03 units c. 3.51 units d. 5.19 units

Explanation:

Step1: Convert angle to radians

To use the arc length formula, convert the central angle from degrees to radians. The conversion formula is $\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$.
$\theta = 81^\circ \times \frac{\pi}{180} = 1.4137$ radians

Step2: Recall arc length formula

The arc length formula is $s = r\theta$, where $s$ is arc length, $r$ is radius, and $\theta$ is the central angle in radians. Rearrange to solve for $r$: $r = \frac{s}{\theta}$.

Step3: Substitute values and calculate

Plug in $s=7.34$ and $\theta=1.4137$ into the rearranged formula.
$r = \frac{7.34}{1.4137} \approx 5.19$

Answer:

D. 5.19 units