A media room is $5.2\text{ m}$ long. A viewer sits at $X$, a horizontal distance $d\text{ m}$

Question

A media room is $5.2\text{ m}$ long. A viewer sits at $X$, a horizontal distance $d\text{ m}$ from the screen wall. The viewer's eye is $1.18\text{ m}$ above the floor and the centre of the screen at $Y$ is $1.74\text{ m}$ above the floor. Two speaker acoustic centres, $P$ and $Q$, are at ear height on the back wall and are $3.2\text{ m}$ apart. The seat lies on the perpendicular bisector of $PQ$. Give non-exact numerical answers correct to $3$ significant figures. Find the angle of elevation from $X$ to $Y$ when $d=1.8$.[2] For comfortable viewing, the angle of elevation must be less than $14^\circ$. Find the range of suitable values of $d$.[2] For balanced sound, $P$, $Q$ and $X$ should form an equilateral triangle. Find the corresponding value of $d$, and determine whether it also satisfies the viewing condition.[4]

Accepted Answer

(a) $17.3^\circ$ (b) $d>2.25\text{ m}$ (c) $d=2.43\text{ m}$, and the viewing condition is satisfied

Solution:

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