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| PAGE: 539 | SET: Exercises | PROBLEM: 51 |
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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