Question

find the radius of a circle which had a sector of area 15 square feet determined by a central angle 1/2 radian.

Answer 1

radius = 7.746 feet

Explanation:$\begin{gathered} \text{Area of sector with angle in degr}ees\colon \\ Areaofasector=\theta/360\times\pi r^{2} \end{gathered}$

the angle is in radian:

$\text{Area of sector = 1/2 }r^2\text{ }\theta$$\begin{gathered} Areaof\text{ sector = 15 square f}eet \\ \theta\text{ = 1/2 radian} \\ 15\text{ = }\frac{1}{2}\times r^2\times\frac{1}{2} \end{gathered}$$\begin{gathered} 15\text{ = }\frac{r^2}{4} \\ 15(4)=r^2 \\ 60=r^2 \end{gathered}$$\begin{gathered} r\text{ = }\sqrt[]{60} \\ r\text{ = 7}.746\text{ f}eet \end{gathered}$