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 = 19 feet; central angle, θ = 340°
s = □ feet
(simplify your answer. type an exact answer in terms of π. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall the arc length formula for a circle with central angle in degrees.

The formula for the length of an arc \( s \) of a circle with radius \( r \) and central angle \( \theta \) (in degrees) is \( s=\frac{\theta}{360^{\circ}}\times2\pi r \).

Step2: Substitute the given values into the formula.

We are given \( r = 19 \) feet and \( \theta=340^{\circ} \). Substituting these values into the formula:

$$ s=\frac{340^{\circ}}{360^{\circ}}\times2\pi\times19 $$

Step3: Simplify the expression.

First, simplify \( \frac{340}{360}=\frac{17}{18} \). Then:

$$ s=\frac{17}{18}\times38\pi=\frac{646\pi}{18}=\frac{323\pi}{9} $$

Answer:

\(\frac{323\pi}{9}\)