Exercise 7 Page 749

In the given diagram we want to find the measure of the arc BC.

Note that the BB' is a diameter, and also that BC and CB' are adjacent arcs. Let's recall the Arc Addition Postulate.

In this case, the arc formed by these two adjacent arcs is a diameter and has an arc measure of 180. mBC+mCB'=180^(∘) According to the diagram mCB'= 168^(∘). Let's substitute this value in the above equation and solve for mBC.

mBC+mCB'=180

Substitute

mCB'= 168

mBC+ 168=180

SubEqn

LHS-168=RHS-168

mBC= 12

We found that BC measures 12^(∘). Let's recall the formula for finding the length of an arc.

We know that the circle's diameter is 21 cm. To find the radius we can divide the diameter by 2. r=21/2= 11.5 Let's substitute 12 for θ and 11.5 for r in the formula to find the arc length.

l=θ/360^(∘)* 2π r

SubstituteII

θ= 12, r= 11.5

l=12/360^(∘)* 2π ( 11.5)

UseCalc

Use a calculator

l=2.19911...

RoundDec

Round to 2 decimal place(s)

l≈ 2.20

The length of the arc rounded to the nearest hundredth is 2.20 cm, which matches answer B.