The length of the radius of a circle is 12 cm at the measure of a central angle, alpha, is 5pi/6. What is the length of the intercepted arc?
whole circle = 2π(12) = 24π
arc/24π = (5π/6) / (2π)
arc = 10π
Thank you!
To find the length of the intercepted arc, we need to use the formula:
Arc Length = (Central Angle / 2π) x 2πr
Where:
- Arc Length is the length of the intercepted arc.
- Central Angle is the measure of the angle in radians.
- r is the radius of the circle.
We are given that the radius (r) is 12 cm and the measure of the central angle (α) is 5π/6. Now let's plug in these values into the formula:
Arc Length = (5π/6 / 2π) x 2π(12)
= (5π/6 / 2π) x 24π
= (5/6) x 24π
Now, simplifying the expression:
Arc Length = (20π) cm
So, the length of the intercepted arc is 20π cm.