Respuesta :
Answer:
The central angle measure of the sector in radians is [tex]\theta=\frac{13}{9}[/tex].
Step-by-step explanation:
A sector of a circle is the portion of a circle enclosed by two radii and an arc. It resembles a "pizza" slice.
The area of a sector when the central angle is in radians is given by
[tex]A=(\frac{\theta}{2})\cdot r^2[/tex]
where
r = radius
θ = central angle in radians
We know that the area of the sector is [tex]26 \:cm^2[/tex] and the radius is 6 cm. Applying the above formula and solving for the central angle ([tex]\theta[/tex]) we get that
[tex]26=(\frac{\theta}{2})\cdot (6)^2\\\\\left(\frac{\theta}{2}\right)\left(6\right)^2=26\\\\\frac{\frac{\theta}{2}\cdot \:6^2}{36}=\frac{26}{36}\\\\\frac{\theta}{2}=\frac{13}{18}\\\\\theta=\frac{13}{9}[/tex]
