Questions: Find the length to three significant digits of the arc intercepted by a central angle θ in a circle of radius r. r=17.4 in., θ=169°

Solution Steps

To find the arc length, we first convert the central angle from degrees to radians. The conversion formula is:

\[ \theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180} \]

Given \(\theta_{\text{degrees}} = 169\), we have:

\[ \theta_{\text{radians}} = 169 \times \frac{\pi}{180} \approx 2.950 \]

The formula for the arc length \(L\) is:

\[ L = r \times \theta_{\text{radians}} \]

Substituting the given values \(r = 17.4\) and \(\theta_{\text{radians}} \approx 2.950\):

\[ L = 17.4 \times 2.950 \approx 51.32 \]

Final Answer