# 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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