Question

An arc in a circle with a radius of 4 inches is subtended by a central angle that measures 110°.

Explain how to find the arc length exactly, and then approximate the length to one decimal place.

Answer 1

7.7 in.

Explanation:

Convert 110 to radians.

110 (π/180) = 11π/18

Multiply 11π/18 and 4 which equals 22π/9

22π/9 = 7.7 in.

Answer 2

circumference of entire circle = 2 * PI * radius
circumference of entire circle = 25.1327412287 inches

110 degree central angle = (110 / 360) = 0.3055555556 of the entire circle

So, 25.1327412287 * 0.3055555556 = 7.6794487099 inches is the length of the subtended arc
ROUNDED = 7.7 inches