Question

1. consider a circle centered at the origin in the xy plane. an angle of measure 0.8π radians in standard position has a terminal ray intersects at point r. the angle is subtended by an arc of the circle in quadrant ii with length 16.9 units. what is the radius of the circle?

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: Rearrange to solve for $r$

$r = \frac{s}{\theta}$

Step3: Substitute given values

Substitute $s = 16.9$ and $\theta = 0.8\pi$:
$r = \frac{16.9}{0.8\pi}$

Step4: Calculate the value

$r = \frac{16.9}{2.5133} \approx 8.45$

Answer:

8.45 units