Exercise 55 Page 666

The length of an arc of a circle is the product of the measure of the arc divided by 360 and the circumference of the circle. length of AB=mAB/360 * π d Therefore, to find the length of the desired arc we first need to find its measure. The measure of an arc is equal to the measure of its corresponding central angle.

Note that the angle measuring 60 and ∠ AOB are supplementary. With this information, we can say that the central angle that corresponds to our arc measures 120. Therefore, the measure of our arc is also 120.

We can also see that the diameter of the circle is 30 centimeters. We can substitute mAB= 120 and d=30 in the formula for arc length and simplify.

Length of AB=mAB/360 * π d

SubstituteII

mAB= 120, d= 30

Length of AB=120/360 * π (30)

▼

Evaluate right-hand side

CommutativePropMult

Commutative Property of Multiplication

Length of AB=120/360 * 30π

MoveRightFacToNum

a/c* b = a* b/c

Length of AB=3600π/360

MovePartNumRight

a* b/c=a/c* b

Length of AB=3600/360 * π

CalcQuot

Calculate quotient

Length of AB=10π

The length of the arc is 10π centimeters.