Answer :
Answer:
The angle of the sector = 86°
Step-by-step explanation:
To find the measure of the angle of the sector, we can use this formula:
[tex]\boxed{A=\frac{\theta}{360^o}\times \pi r^2 }[/tex]
where:
- [tex]A[/tex] = area of sector
- [tex]\theta[/tex] = angle of sector
- [tex]r[/tex] = radius
Given:
- [tex]A[/tex] = 48 in²
- [tex]r[/tex] = 8 in
Then:
[tex]\displaystyle A=\frac{\theta}{360^o}\times \pi r^2[/tex]
[tex]\displaystyle 48=\frac{\theta}{360^o}\times 3.14 \times 8^2[/tex]
[tex]\displaystyle \theta=\frac{48}{3.14\times64} \times 360^o[/tex]
[tex]\bf\theta=86^o[/tex]
