In circle S with mangle RST=126^circ and RS=6 units, find the length of overparen (RT) Round to the nearest hundredth. square T s

To find the length of the arc \(\overparen{RT}\) in circle \(S\), we can use the formula for the length of an arc, which is given by:<br /><br />\[<br />\text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r<br />\]<br /><br />where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle.<br /><br />Given:<br />- \(m\angle RST = 126^\circ\)<br />- \(RS = 6\) units (which is the radius of the circle)<br /><br />Substitute these values into the formula:<br /><br />\[<br />\text{Arc Length} = \frac{126}{360} \times 2\pi \times 6<br />\]<br /><br />Simplify the fraction:<br /><br />\[<br />\frac{126}{360} = \frac{7}{20}<br />\]<br /><br />Now calculate the arc length:<br /><br />\[<br />\text{Arc Length} = \frac{7}{20} \times 2\pi \times 6 = \frac{7}{20} \times 12\pi<br />\]<br /><br />\[<br />= \frac{84\pi}{20} = \frac{21\pi}{5}<br />\]<br /><br />Calculate the numerical value:<br /><br />\[<br />\frac{21\pi}{5} \approx 13.1947<br />\]<br /><br />Rounding to the nearest hundredth, the length of \(\overparen{RT}\) is approximately \(13.19\) units.