Question

The area of a sector with a radius of 14 yards is 38.28 square yards. Calculate the approximate angle of the sector. Round to the nearest tenth.

Answer 1

Given that:
Area of sector,A = 38.28 square yards
Radius, r=14 yards
Formula for area of sector:

`A= (\theta)/(360^0) * \pi r^2`
Put values

`38.28= (\theta)/(360^0) * (3.14)(14)^2`
Solve for Angle theta.
38.28 x 360 = θ x (3.14)(14)²
13780.8=615.44 θ
Divide both sides by 615.44
22.4°=θ
or
θ=22.4°

Answer: Angle is 22.4°