Hello there. To solve this question, we'll have to remember some properties about arcs and angles in a circle.
Given the arc AB in the following circle:
We have to determine its length.
For this, remember that given an arc, the angle and the radius of the circle, we can find its length in the following way:
Where C is the length of the circumference, given by the formula:
[tex]C=2\pi R[/tex]
Such that we get:
Of course, the angle alpha is in radians. To convert an angle in degrees to radians, we apply the formula:
Therefore, we apply this formula by plugging Angle = 30º:
[tex]\alpha=30^{\circ}\cdot\frac{\pi}{180^{\circ}}=\frac{\pi}{6}[/tex]
Now, we plug this angle in the formula, also plugging R = 6 in, such that
This is the length of this arc.
