Arc Length

• Start with the formula for radian measure …

… and multiply both sides by r to get …

s

r

r s

s rArc length = radius times angle measure in radians.

Example 1:A circle has a radius of 7 in. Find the length of the arc subtended by a central angle of 4 rad.

Arc length = radius times angle measure in radians.

s r

7 4

28 inches

Example 2:A circle has a radius of 6cm. Find the length of the arc subtended by a central angle of 52°.

180 radians

• Since the formula for arc length uses radian measure, we first change the degree measure to radians.

5252 rad

1 180

13 rad

45

13 52 rad

45

Arc length = radius times angle measure in radians.

s r

136

45

26cm

15

1.73cm