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Find the measure of CD.
Round to the nearest tenth.
mCD=[?]degrees

Find The Measure Of CD Round To The Nearest Tenth MCDdegrees class=

Sagot :

Answer:

m(arc CD) = 14.1 cm

Step-by-step explanation:

Measure of an arc of the circle = [tex]\frac{\theta}{360}(2\pi r)[/tex]

Here 'r' = radius of the circle

θ = Angle subtended by the arc at the center of the circle

From triangle OED,

sin(∠EOD) = [tex]\frac{ED}{OD}[/tex]

sin(∠EOD) = [tex]\frac{\frac{12.7}{2}}{9.06}[/tex]

                 = [tex]\frac{6.35}{9.06}[/tex]

                 = 0.7

m∠EOD = 44.498

              ≈ 44.5°

Angle subtended by the arc CD at the center = m∠COD

                                                                            = 2(44.5)

                                                                            = 89°

m(arc CD) = [tex]\frac{89}{360}(2\pi)(9.06)[/tex]

                 = 14.07

                 ≈ 14.1 cm

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