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circle has center C, as shown below, and diameter 32 cm. Find the length of AB if m∠ABC = 90°Part I: What fractional part of the circle's circumference is AB?Part II: Use the fraction you determined in Part I and the circumference formula to find the length of AB. Show your work and round your answer to the nearest hundredth.

circle has center C as shown below and diameter 32 cm Find the length of AB if mABC 90Part I What fractional part of the circles circumference is ABPart II Use class=

Respuesta :

Given:

[tex]\begin{gathered} m\angle ACB=90 \\ \text{Diameter}=32 \end{gathered}[/tex][tex]\begin{gathered} \text{Radius}=\frac{\text{Diameter}}{2} \\ r=\frac{32}{2} \\ r=16 \end{gathered}[/tex][tex]\begin{gathered} AB=\frac{mAB}{360}\times2\pi r \\ AB=\frac{90}{360}\times2\pi(16) \\ AB=\frac{1}{4}\times32\pi \\ =8\pi \\ =25.132 \end{gathered}[/tex]

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