Question

Photo question; find the length

Answer 1

`\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`

Answer 2

`\boxed{\textbf{26.9 m}}`

Explanation:

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

`s = r\theta * \frac{\pi  }{180^{^(\circ)}}`

where θ is measured in degrees.

Data:

r = 11.4 m

θ = 135°

Calculation:

`s = \text{11.4 m} * 135^{^(\circ)}*\frac{\pi}{180^{^(\circ)}} = \textbf{26.9 m}\\\\\text{The length of the arc is }\boxed{\textbf{26.9 m}}`