The cone and the triangle

Geometry Level 4

Not drawn to scale

Not drawn to scale

In the picture, we're given an unrotated hyperbola centered at the origin. The slightly bolded box (whose vertices are intersected by the asymptotes of the graph) is defined such that the major axis is the height of the box and the minor axis is the width of the box. \( B \) is located at a vertex of that box such that both coordinates are positive.

If the slopes of the asymptotes are 2016 and -2016, and point \(C\) is located at a focus of the hyperbola, and \( AC = 1 \), let the measure of angle \(ABC\), the purple angle, in degrees, equal \( \delta\). Find \( \left \lfloor 10000 \delta \right \rfloor \). Use wolfram alpha to compute the answer.


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