The diagram shows part of a map of a small town. Joel's house is located at point W, the childcare centre at point X, the park at point Y and the shopping mall at point Z. WZ = 4.6 km, YZ = 2.5 km and XY = 3.4 km The bearing of W from Y is 043.4° and the bearing of X from Y is 064.1°.

1. Find the reverse bearing from $X$ to $Y$.

Bearing of $X$ from $Y = 064.1^\circ$.

Therefore, bearing of $Y$ from $X$ is
$064.1^\circ + 180^\circ = 244.1^\circ.$

1. Identify the horizontal distance corresponding to the smallest angle of depression.

The smallest angle of depression occurs when the horizontal distance from $Z$ to the point on path $WY$ is greatest.

Since $WZ=4.6\text{ km}$ and $YZ=2.5\text{ km}$, the furthest point on the path from $Z$ is $W$.

So the horizontal distance is
$4.6\text{ km}.$

2. Use the tangent ratio to find the height of the shopping mall.

Let the height of the shopping mall be $h$ km.

Using $\tan \theta=\dfrac{\text{opposite}}{\text{adjacent}}$,
$\tan 25^\circ=\frac{h}{4.6}$
$h=4.6\tan 25^\circ$
$h=2.145\ldots\text{ km}$

Converting to metres,
$2.145\ldots\text{ km}=2145\ldots\text{ m}$

To the nearest metre,
$h=2145\text{ m}.$