math

For a circle with a diameter of 6 meters,

what is the measurement of a central angle (in degrees) subtended by an arc with a length of 5.2 π meters?

Let radius r = 3 meters

Let arc = \(5.2\pi \) meters

Let angle subtended by the arc at the centre = \(\alpha\)

\(\begin{array}{|rcll|} \hline \text{Formula: } ~ arc &=& 2\cdot \pi \cdot r \cdot \frac{\alpha}{360^{\circ}} \\\\ 5.2\pi\ m &=& 2\pi \cdot 3\ m \cdot \frac{\alpha}{360^{\circ}} \\ 5.2\pi &=& 2\pi \cdot 3 \cdot \frac{\alpha}{360^{\circ}} \\ 5.2\pi &=& 6\pi \frac{\alpha}{360^{\circ}} \quad & | \quad :\pi \\ 5.2 &=& 6 \frac{\alpha}{360^{\circ}} \quad & | \quad \cdot 360^{\circ} \\ 5.2 \cdot 360^{\circ} &=& 6 \alpha \quad & | \quad :6 \\ 5.2 \cdot 60^{\circ} &=& \alpha \\ 312^{\circ} &=& \alpha \\ \hline \end{array}\)

 The measurement of a central angle (in degrees) is \(312^{\circ} \)