Question

The sector of a circle of radius 7.5ft has an area of 13ft^2. Find the central angle of the sector. Do not round any intermediate computations. Round your answer to the nearest tenth.__ radians

Answer 1

Given:

`\begin{gathered} A=13ft^2 \\ r=7.5\text{ ft} \end{gathered}`

The area of a sector is given by

`\begin{gathered} A=(\emptyset)/(360^(\circ))\ast\pi\ast r^2 \\ \text{Here }\emptyset\text{ is the central angle of the sector and r is the radius of circle} \\ \text{The equation can rewritten as} \\ \emptyset=(A)/(\pi\ast r^2)\ast360^(\circ) \end{gathered}`

Substitute the given values.

`\begin{gathered} \emptyset=(13)/(\pi\ast7.5^2)\ast2\pi \\ \emptyset=\frac{13}{56.25^{}}\ast2=0.46radians\cong0.5\text{ radians} \end{gathered}`

The central angle is 0.5 radians.