Question

find the length of the arc, s, on a circle of radius r intercepted by a central angle θ. express arc length in terms of π. then round your answer to two decimal places. radius, r = 12 feet; central angle, θ = 330° s = \square feet (simplify your answer. type an exact answer in terms of π. use integers or fractions for any numbers in the expression.) s = \square feet (round to two decimal places as needed.)

Explanation:

Step1: Convert degrees to radians

$\theta = 330^\circ \times \frac{\pi}{180^\circ} = \frac{11\pi}{6}$

Step2: Apply arc length formula

$s = r\theta = 12 \times \frac{11\pi}{6}$

Step3: Simplify exact expression

$s = 22\pi$

Step4: Calculate decimal approximation

$s = 22 \times 3.14159 \approx 69.115$

Step5: Round to two decimals

$s \approx 69.12$

Answer:

$s = 22\pi$ feet
$s = 69.12$ feet