The area of a sector is 110.60 sq yd and the radius of the sector is 10.82 yd. What is the measure of the central angle rounded to the nearest tenth?
The formula for the area of a sector is given by:
Area of sector = (θ/360) * π * r²
Where θ is the central angle in degrees and r is the radius.
We can rearrange the formula to solve for θ:
θ = (360 * Area of sector) / (π * r²)
Plugging in the given values:
θ = (360 * 110.60) / (π * (10.82)²)
θ ≈ 102.8 degrees
Therefore, the measure of the central angle rounded to the nearest tenth is 102.8 degrees.