Question

a circular arc has measure 12 in and is intercepted by a central angle of 1.7 radians. find the radius r of the circle
do not round any intermediate computations, and round your answer to the nearest tenth.
$r = \square$ in

Explanation:

Step1: Recall arc length formula

The formula for arc length $s$ is $s = r\theta$, where $r$ is radius, $\theta$ is central angle in radians.

Step2: Rearrange for radius $r$

Isolate $r$ by dividing both sides by $\theta$:
$r = \frac{s}{\theta}$

Step3: Substitute given values

Substitute $s=12$ in, $\theta=1.7$ radians:
$r = \frac{12}{1.7}$

Step4: Calculate and round to nearest tenth

Compute the value and round:
$r \approx 7.1$

Answer:

$r = 7.1$ in