SOLUTION
Step 1: Let us draw a pictorial view of the information given:
The height of the antenna AB will be:
[tex]AB=OB-OA[/tex]Let us find OA from triangle OAS
[tex]\begin{gathered} \tan 34=\frac{OA}{19} \\ OA=19\times\tan 34 \\ OA=12.816m \end{gathered}[/tex]Now, we will find OB from triangle OBS
[tex]\begin{gathered} \tan 41=\frac{OB}{19} \\ OB=19\times\tan 41 \\ OB=16.516m \end{gathered}[/tex]Now, let us find length AB, which is the length of the antenna:
[tex]\begin{gathered} AB=OB-OA \\ AB=16.516m-12.816m \\ AB=3.7m \end{gathered}[/tex]The height of the antenna is 3.7 meters.
