# How to plot a cone of view mathematically?

How to plot a cone of view mathematically? Like the below example. I need to plot it mathematically to exactly be able to get the answer for something like "What detection distance (in percent) is the detector rated at when viewing a fire at a 27.23 degree angle?

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Full image here

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I'm not sure if this is what you are asking for because your image is broken but anyway:

A right circular cone in 3d is an affine transformation of the set of points that satisfy $z=|x,y|=\sqrt{x^2+y^2}$

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