Find me in depths of darkness

Geometry Level 3

A person standing by the side of a road observes a row of equidistant telephone poles of equal height. Neglecting the height of the person's eye, the 10th and the 17th poles subtend the same angle that they would have subtended if they were in the position of first pole and were respectively \(\frac{1}{2}\) and \(\frac{1}{3}\) of their common height.

Find the secant of the angle between the base line of the poles and the lines drawn from the person's eye to the base of the first pole.

NOTE:-Let\[\sec \theta = \frac{-2\sqrt{a}}{b}\]. Then find a+b.

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