Positioning an outdoor sound zone

Two loudspeakers \(P\) and \(Q\) are \(18\text{ m}\) apart along a straight fence. A listener at \(X\) stands on the perpendicular bisector of \(PQ\).

A vertical lighting mast \(9\text{ m}\) high stands at the midpoint \(M\) of \(PQ\).

Give non-exact numerical answers correct to \(3\) significant figures.

1. Find the angle of elevation of the mast top from \(X\) when \(XM=12\text{ m}\).[2]
2. For eye comfort, the angle of elevation must be less than \(32^\circ\). Find the range of allowed values of \(XM\).[2]
3. For balanced sound, triangle \(PXQ\) should be equilateral.
   Find \(XM\) for this arrangement and determine whether it satisfies the eye-comfort condition.[4]