# 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?

$\hskip0.9in$

Full image here

-

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