In a circle with a radius of 2.8 cm, an arc is intercepted by a central angle of π5 radians. What is the arc length?

Accepted Solution

Answer: The length of the arc is about 1.758 cm.

First, we need to determine the size of the angle. If we have pi/5 radians, we can convert that to 36 degrees, because pi radians is 180 degrees. Now, we know the measure of the arc is 36 degrees. 36 degrees out of 360 degrees is 10%.

Our arc is 10% of the circumference of the circle.

The circumference is 2(pi)r or 2(3.14)2.8 = 17.58 cm

Now, multiply 17.58 by 0.1 to get a total of 1.758 cm.