A security light mounted above a house illuminates part of a circular region defined by

and .

The area of a sector of a circle with radius and central angle is .

Where is measured in radians.

The total area of the region is approximately .

The area of the region described is the difference of the areas of two sectors.

Both sectors have an angle measure of .

By solving ,we get .

The larger radius is and the smaller radius is .

Calculate the by substituting the values of and .

The total area of the region is approximately .

Substitute this value in for in the equation above and solve for .

Since is not in negative, it is not considered.

Therefore, the value of is .

The value of is .

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