An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle? Round your answer to the nearest tenth.

Given:

Arc length = 8 inches

radius = 3 inches

find the measure of the central angle.

Arc length = radius * central angle

central angle = arc length / radius

central angle = 8 inches / 3 inches

central angle = 2.667 (radian)

Central angle in degrees = 152.88°

Circumference of the circle = 2 * 3.14 * 3 inches = 18.84 inches

1 circle = 360° / 18.84 inches = 19.11° per inch

19.11° per inches * 8 inches of arc length = 152.88°