Given that:
Area of sector,A = 38.28 square yards
Radius, r=14 yards
Formula for area of sector:
[tex]A= \frac{\theta}{360^0} \times \pi r^2 [/tex]
Put values
[tex]38.28= \frac{\theta}{360^0} \times (3.14)(14)^2 [/tex]
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°
