Question

watch the video and then solve the problem given below. click here to watch the video. find the length of the arc, s, on a circle of radius r intercepted by a central angle θ. express the arc length in terms of π. then round your answer to two decimal places. radius, r = 15 inches; central angle, θ = 55°. s = inches (simplify your answer. type an exact answer in terms of π. use integers or fractions for any numbers in the expression.) s = inches (round to two decimal places as needed.)

Explanation:

Step1: Convert angle to radians

First, convert the angle $\theta = 55^{\circ}$ to radians. The conversion formula is $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. So, $\theta = 55\times\frac{\pi}{180}=\frac{11\pi}{36}$ 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 $r = 15$ inches and $\theta=\frac{11\pi}{36}$ radians, then $s=15\times\frac{11\pi}{36}=\frac{55\pi}{12}$ inches.

Step3: Round the answer

Now, calculate the decimal value of $s$. $s=\frac{55\pi}{12}\approx\frac{55\times 3.14159}{12}\approx14.43$ inches.

Answer:

$\frac{55\pi}{12}$ inches
$14.43$ inches