Question

calculati masura arcului de cerc cunoscand lungimea sa lungimea arcului=10pi si raza cercului=9

Answer 1

   
[tex]\texttt{Se da: } \\ \\ \overset{\frown}{AB} = \texttt{arcul de cerc} \\ l(\overset{\frown}{AB} ) = 10\pi~cm ~~~~~~~\texttt{(Lungimea arcului)} \\ R = 9 ~cm ~~~~~~~\texttt{(Raza cercului)} \\ l(C) = 2\pi R~~~~~~~\texttt{(Lungimea cercului)}\\ \\ \texttt{Se cere: } \\ \\ m(\overset{\frown}{AB}) = ? ~~~~~~~\texttt{(Masura arcului)} [/tex]


[tex]\displaystyle \\ \texttt{Rezolvare: } \\ \\ m(\overset{\frown}{AB}) = 360 \times \frac{l(\overset{\frown}{AB} )}{l(C)} = 360 \times \frac{10\pi }{2\pi R} = \\ \\ = 360 \times \frac{10\pi }{2\pi \times 9} = 360 \times \frac{10\pi }{18\pi} = \frac{360 \times 10\pi }{18\pi} = 20 \times 10 = \boxed{200^o}[/tex]