Final answer:
To calculate the arc length intercepted by an 80° angle in a circle with a 21 mm radius, use the formula As = (θ/360) × 2πr. Upon computing, the arc length equals approximately 29.321 millimeters.
Step-by-step explanation:
To find the arc length intercepted by a central angle in a circle, the formula is:
As = (\u03B8/360) \u00d7 2\u03C0r
Where \u03B8 is the central angle in degrees, \u03C0 is Pi (approximately 3.14159), and r is the radius of the circle. In this question:
- \u03B8 = 80 degrees
- r = 21 millimeters
Using the formula for arc length, we get:
As = (80/360) \u00d7 2\u03C0\u00d7 21
Calculate the numerical value:
As = (1/4.5) \u00d7 (2 \u00d7 3.14159 \u00d7 21)
As = (2 \u00d7 3.14159 \u00d7 21) / 4.5
As = 29.321 millimeters (approx)
The length of the arc intercepted by a central angle that measures 80\u00b0 for a circle with a radius of 21 millimeters is approximately 29.321 millimeters.