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

Respuesta :

Given:

[tex]\begin{gathered} A=13ft^2 \\ r=7.5\text{ ft} \end{gathered}[/tex]

The area of a sector is given by

[tex]\begin{gathered} A=\frac{\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=\frac{A}{\pi\ast r^2}\ast360^{\circ} \end{gathered}[/tex]

Substitute the given values.

[tex]\begin{gathered} \emptyset=\frac{13}{\pi\ast7.5^2}\ast2\pi \\ \emptyset=\frac{13}{56.25^{}}\ast2=0.46radians\cong0.5\text{ radians} \end{gathered}[/tex]

The central angle is 0.5 radians.

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