Question

find the length s of the arc that subtends a central angle of measure 90° in a circle of radius 19 m. (round your answer to two decimal places.) s = m

Explanation:

Step1: Convert angle to radians

We know that $90^{\circ}=\frac{\pi}{2}$ radians.

Step2: Use arc - length formula

The arc - length formula is $s = r\theta$, where $r$ is the radius and $\theta$ is the central angle in radians. Given $r = 19$ m and $\theta=\frac{\pi}{2}$, then $s=19\times\frac{\pi}{2}$.

Step3: Calculate the value

$s=\frac{19\pi}{2}\approx\frac{19\times 3.14159}{2}= 29.845105\approx29.85$ m.

Answer:

$29.85$