Question

the figure gives an angle in standard position with measure 0.687π and a circle with radius 3 in the xy - plane. what is the length of the minor arc of the circle from point c to point b, the arc subtended by the angle?
a 0.719
b 2.158
c 6.475
d 9.712

Explanation:

Step1: Recall arc length formula

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

Step2: Substitute given values

Here, $r = 3$ and $\theta = 0.687\pi$. Substitute into the formula:
$s = 3 \times 0.687\pi$

Step3: Calculate the result

First compute $3 \times 0.687 = 2.061$, then multiply by $\pi$:
$s = 2.061 \times 3.1416 \approx 6.475$

Answer:

C. 6.475