Answered

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The area of a sector is 48 in^2. If the radius is 8 in, what is the measure of the angle of the sector?
86°
172°
125°
92°

Sagot :

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]

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