The total height of the building will be calculated as
[tex]H=y+123m[/tex]Step 1: Calculate y using the trigonometric ratio tan
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \text{where,} \\ \theta=82^0 \\ \text{opposite}=DB=y \\ \text{adjacent}=AB=40m \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \tan 82^0=\frac{y}{40m} \\ \text{cross multiply, we will have} \\ y=40\times\tan 82^0 \\ y=284.6m \\ y\approx285m \end{gathered}[/tex]Therfore,
The height of the building will be
[tex]\begin{gathered} H=y+123m \\ H=285m+123m \\ H=408m \end{gathered}[/tex]Hence,
The Approximate height of the building = 408m
