# Math

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A sensor light installed on the edge of a home can detect motion for a distance of 50ft. in front and with a range of motion of 192degree. Over what area will the sensor detect motion and become illuminated?

• Math -

Area = area of full circle * (θ/360)
=πr^2*θ/360
=π 50^2*192/360
=4000/3 ft^2.

• Trigonometry -

making correction in just the answer all procedures are well done !!

Area = area of full circle * (θ/360)
=πr^2*θ/360
=π 50^2*192/360
= 4188.79 ft^2

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