Question

If a central angle of measure 30 degrees is subtended by a circular arc of length 6 meters, as is illustrated below, how many meters in length is the radius of the circle?

Answer 1

Answer on Question #48595 – Math – Geometry

If a central angle of measure 30 degrees is subtended by a circular arc of length 6 meters, as is illustrated below, how many meters in length is the radius of the circle?

Solution:

$\theta = 30{}^{\circ}$ – central angle of the circle;

$S = 6m$ – length of the circular arc;

$R$ – radius of the circle;

Formula for the length of the circular arc:

$$S = \frac{\theta}{180{}^{\circ}} \pi R$$

Thus, the radius is equal to

$$R = \frac{S}{\frac{\theta}{180{}^{\circ}} \pi} = \frac{180{}^{\circ} \cdot S}{\theta \pi} = \frac{180{}^{\circ} \cdot 6m}{30{}^{\circ} \cdot 3.14} = 11.5 \, m$$

Answer: radius of the circle is equal to $11.5 \, m$.

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