To convert radians to degrees, we use the formula:
[tex]\[
\text{degrees} = \text{radians} \times \left(\frac{180}{\pi}\right)
\][/tex]
Given the radian measure is [tex]\(5\)[/tex] and [tex]\(\pi\)[/tex] is approximated as [tex]\(3.1416\)[/tex], we can substitute these values into the formula.
First, calculate the conversion factor:
[tex]\[
\frac{180}{\pi} = \frac{180}{3.1416}
\][/tex]
Next, multiply the given radian measure by this conversion factor:
[tex]\[
\text{degrees} = 5 \times \left(\frac{180}{3.1416}\right) = 5 \times 57.2958
\][/tex]
Perform multiplication:
[tex]\[
\text{degrees} = 286.4782
\][/tex]
We need to round this result to the nearest hundredth:
[tex]\[
\text{Rounded degrees} = 286.48
\][/tex]
Therefore, the radian measure of 5 radians converts to approximately [tex]\(286.48^{\circ}\)[/tex] when rounded to the nearest hundredth.
Out of the provided options, [tex]\(286.48^{\circ}\)[/tex] is the correct answer.
