Page 158 - Math Course 3 (Book 2)
P. 158

Circles: Angles and Arcs




        Arc Length
                                                            Your Turn!

            Example                                        Circle Graphs

                                                            SPEED LIMITS
         In ⊙B, AC = 9 and m∠ABD = 40.                      This graph shows the percent of U.S. states that
                                                            have each speed limit on their interstate highways.
         Find the length of AD.                             Find the measurement of the central angles
                                                            representing each category. List them from
                                                            least to greatest.
                 A           B



                                         C
                 D



         In ⊙B, AC = 9 so C = π(9) or 9π and mAD = m∠ABD
         or 40. Write a proportion to compare each part to its
         whole.


           degree                                           A. 3.6°, 72°, 64.8°, 39.6°
          measure                                           B. 3.6°, 39.6°, 64.8°, 72°
           of arc   →   40        ℓ   ← arc length          C. 7.2°, 144°, 129.6°, 79.2°
           degree    →  360  =   9π   ← circumference       D. 7.2°, 79.2°, 129.6°, 144°
          measure
          of whole
           circle                                             Answer

         Now solve the proportion for ℓ.                    This graph shows the percent of U.S. states that
                                                            have each speed limit on their interstate highways.
               40       ℓ                                   Is the arc for the wedge for 65 mph congruent to
              360   =  9π                                   the combined arcs for the wedges for 55 mph and
                                                            70 mph?
          40
          360  (9π) = ℓ     Multiply each side by 9 π.      A. yes
                                                            B. no
                      π = ℓ  Simplify.                      C. cannot be determined


                                                              Answer
            Answer       The length of AD is π units or
                              about 3.14 units.



        Arc Length

         In ⊙A, AY = 21 and m∠XAY = 45. Find the length of WX to the nearest hundredth.

         A. 7.88
         B. 15.75                                                           W                       X
         C. 49.48
         D. 24.74
                                                                            Z           A           Y
           Answer



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