Respuesta :

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =135\\ r=11.4 \end{cases}\implies s=\cfrac{\pi (135)(11.4)}{180}\implies s=8.55\pi \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill s\approx 26.86~\hfill[/tex]

znk

Answer:

[tex]\boxed{\textbf{26.9 m}}[/tex]

Step-by-step explanation:

The formula for the arc (s) of a circle is

[tex]s = r\theta \times \dfrac{\pi  }{180^{^{\circ}}}[/tex]

where θ is measured in degrees.

Data:

r = 11.4 m

θ = 135°

Calculation:

[tex]s = \text{11.4 m} \times 135^{^{\circ}}\times\dfrac{\pi}{180^{^{\circ}}} = \textbf{26.9 m}\\\\\text{The length of the arc is }\boxed{\textbf{26.9 m}}[/tex]

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