During a study tour to New Delhi, Shreya, a student whose height is \(1\) \(m\), visited India Gate. Located near Kartavya Path (formerly Rajpath), this \(42\) \(m\) tall monument was earlier called the All India War Memorial. It honours \(74187\) soldiers of the Indian Army who sacrificed their lives in the First World War, and was designed by Sir Edwin Lutyens in the style of Roman triumphal arches.
(i) What is the angle of elevation from Shreya's eye to the top of India Gate, if she is standing at a distance of \(41 \ m\) away from the India Gate?
(ii) If Shreya observes the angle of elevation from her eye to the top of India Gate to be \(60^\circ\), then how far is she standing from the base of the India Gate?
(iii) (A) If the angle of elevation from Shreya's eye changes from \(45^\circ\) to \(30^\circ\), when she moves some distance back from the original position. Find out the distance she moves back.
(B) If Shreya moves to a point which is at a distance of \(\frac{41}{\sqrt{3}} \ m\) from the India Gate, then find out the angle of elevation made by her eye to the top of India Gate.