Math CentralQuandaries & Queries


Question from Frank:

I know we have a field of view of 90 degrees and the distance we can cover is 6 miles. What is the area we can cover/view?
A formula would be nice to have since the diameter or distance of the wedge area can change and the degree of the field of view can also change.
Thank you and I look forward to hearing from you.

Hi Frank,

The area of a circle is π r2 square units where r is the radius in units and π is approximately 3.1416. Thus for a radius of 6 miles the area of the circle is π × 62 = 36 × π = 113.1 square miles. If you have a 90 degree view that is one quarter of the circle so the sector you can view has an area of 113.1/4 = 28.3 square miles.

If the angle of the field of view changes then the proportion of the circle you can view also changes. If the angle of the field of view is a degrees than you can see a/360 of the circle so the area of the sector you can view is (a/360) × (π r2) square units.

I hope this helps,

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