Express answer in exact form.
2 answers:
I'm guessing that you want to find the segment area of a circle that has a radius AO = 8" and a chord AB with a length of 8".
Sine angle AOD = AE / OA
Sine angle AOD = 4 / 8
Sine angle AOD = .5
arc sine (.5) = 30 degrees
So, angle AOB = 60 degrees
Circle Area = PI * radius^2
Circle Area = <span> <span> <span> 201.06</span></span></span>
Sector Area = (60/360) * 201.06
Sector Area = 33.51
Line OE^2 = AO^2 -AE^2
Line OE^2 = 64 -16
Line OE = <span> <span> <span> 6.9282032303 </span> </span> </span>
Triangle AOB Area = OE*AE = <span> <span> <span> 6.9282032303 * 4
</span></span></span>Triangle AOB Area = <span> <span> <span> 27.7128129211 </span> </span> </span>
Segment Area = Sector Area -Triangle AOB Area
Segment Area = 33.51 -<span>27.71
</span>Segment Area = 5.80
Sine angle AOD = AE / OA
Sine angle AOD = 4 / 8
Sine angle AOD = .5
arc sine (.5) = 30 degrees
So, angle AOB = 60 degrees
Circle Area = PI * radius^2
Circle Area = <span> <span> <span> 201.06</span></span></span>
Sector Area = (60/360) * 201.06
Sector Area = 33.51
Line OE^2 = AO^2 -AE^2
Line OE^2 = 64 -16
Line OE = <span> <span> <span> 6.9282032303 </span> </span> </span>
Triangle AOB Area = OE*AE = <span> <span> <span> 6.9282032303 * 4
</span></span></span>Triangle AOB Area = <span> <span> <span> 27.7128129211 </span> </span> </span>
Segment Area = Sector Area -Triangle AOB Area
Segment Area = 33.51 -<span>27.71
</span>Segment Area = 5.80
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