Questions: 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=12 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.)

Solution Steps

To find the length of the arc, $s$, on a circle of radius $r$ intercepted by a central angle $\theta$, we can use the formula: \[ s = r \theta \] where $\theta$ is in radians. First, we need to convert the angle from degrees to radians using the conversion factor: \[ \theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180} \] Then, we can calculate the arc length in terms of $\pi$ and also round it to two decimal places.

To find the arc length, we first convert the central angle from degrees to radians using the formula: \[ \theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180} \] Substituting the given value: \[ \theta_{\text{radians}} = 55 \times \frac{\pi}{180} \approx 0.9599 \]

Next, we use the formula for arc length: \[ s = r \theta \] Substituting the values of \( r = 12 \) inches and \( \theta \approx 0.9599 \): \[ s \approx 12 \times 0.9599 \approx 11.5192 \]

Finally, we round the arc length to two decimal places: \[ s \approx 11.52 \]

Final Answer