Trigonometry! #74

Geometry Level 3

A tower stands at the centre of a circular park. \(A\) and \(B\) are two points on the boundary of the park such that \(AB = a\) subtends an angle of \(60^{\circ}\) at the foot of the tower and the angle of elevation of the top of the tower from \(A\) or \(B\) is \(30^{\circ}\).

If the height of the tower, in terms of \(a\), is \(x\), then enter the value of \(\frac {x}{a}\) correct to three decimal places.

This problem is part of the set Trigonometry.

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