Just elegancy required 3

Geometry Level pending

A tower stands vertically in an inaccessible place. In order to ascertain its height an investigator stations himself on the ground and finds the angle of elevation of the top of the tower to be 30 degrees. then he moves a distance \(d\) in a certain direction and from there he finds the angle of elevation of the top to be same as before. On moving a distance\(\frac{5}{3} d\)at the right angle to his former direction, he finds the elevation of the top to be 60 degrees. Find the height of the tower.

NOTE:-If height could be represented as either\(\sqrt{\frac{p}{q}}\times d or \sqrt{\frac{r}{s}}\times d\).Then find p+q+r+s.

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