Question:
On a circle of radius 6 feet, what angle would subtend an arc of lenght 5 feet?
nswer:
he frormula for the lenght of arc (s) given an angle theta (in radians) and a radius R is:
[tex]S=\theta R[/tex]
We'll just have to clear theta from this equation, and convert it to degrees.
[tex]\begin{gathered} S=\theta R\rightarrow\frac{S}{R}=\theta \\ \theta=\frac{5}{6}\text{ radians} \\ To\text{ convert from radians to degrees, multiply by }\frac{180}{\pi} \\ \theta=\frac{5}{6}\times\frac{180}{\pi}\rightarrow\theta=47.74\text{ degrees} \end{gathered}[/tex]
Therefore, the angle that would subtend an arc of lenght 5 feet on a circle of radius 6 feet is 47.74°
