Exercise 57 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 * 2π r 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. The measure of the arc at the low right of the diagram is 40. Therefore, its corresponding central angle measures 40.

Note that the angle measuring 40 and ∠ AOB are supplementary. With this information, we can find the measure of the central angle that corresponds to our arc. 180 - 40 = 140 Let's update the diagram.

We can also see that the radius of the circle is 36 inches. We can substitute mAB= 140 and r=36 in the formula for arc length and simplify.

Length of AB=mAB/360 * 2π r

SubstituteII

mAB= 140, r= 36

Length of AB=140/360 * 2π (36)

▼

Evaluate right-hand side

CommutativePropMult

Commutative Property of Multiplication

Length of AB=140/360 * 2(36)π

Multiply

Multiply

Length of AB=140/360 * 72π

MoveRightFacToNum

a/c* b = a* b/c

Length of AB=10 080π/360

MovePartNumRight

a* b/c=a/c* b

Length of AB=10 080/360 * π

CalcQuot

Calculate quotient

Length of AB=28π

The length of the arc is 28π inches.