Problem
Consider the hyperbola x2/100 − y2/64 = 1 with foci at S and S1, where S lies on the positive x-axis. Let P be a point on the hyperbola, in the first quadrant. Let ∠SPS1 be α with α < π/2. The straight line passing through the point S and having the same slope as that of the tangent at P to the hyperbola, intersects the straight line S1P at P1. Let δ be the distance of P from the straight line SP1, and β = S1P. Then find the greatest integer less than or equal to (βδ/9)sin(α/2).