A chord of a circle subtends an angle of \(60^\circ\) at the length of a circle of radius 14 cm. Find the length of the chord

Answer Details

To solve this problem, we can use the relationship between the length of a chord and the angle it subtends in a circle. Specifically, if a chord of length $c$ subtends an angle of $\theta$ degrees at the center of a circle of radius $r$, then: $$c = 2r\sin\left(\frac{\theta}{2}\right)$$ In this problem, we are given that the angle subtended by the chord is $60^\circ$ and the radius of the circle is $14$ cm. Thus, we can plug in these values to get: $$c = 2\cdot 14\cdot \sin\left(\frac{60}{2}\right) = 2\cdot 14\cdot \sin(30)$$ Recall that $\sin(30) = \frac{1}{2}$, so we have: $$c = 2\cdot 14\cdot \frac{1}{2} = 14$$ Therefore, the length of the chord is $\boxed{14}$ cm. To summarize, the length of a chord in a circle can be found using the formula $c = 2r\sin\left(\frac{\theta}{2}\right)$, where $r$ is the radius of the circle and $\theta$ is the angle subtended by the chord at the center of the circle. Applying this formula to the given problem, we find that the length of the chord is 14 cm.