In triangle ABC,
[tex]\begin{gathered} \tan 74^{\circ}=\frac{AB}{BC} \\ \tan 74^{\circ}=\frac{AB}{12\text{ ft}} \\ AB=12\tan 74^{\circ}\text{ ft} \\ AB=41.84\text{ ft.} \end{gathered}[/tex]
The height of the top of the goal post can be determined as,
[tex]\begin{gathered} h=6\text{ ft+AB} \\ =6\text{ ft+41.84 ft} \\ =47.84ft \end{gathered}[/tex]
Thus, the required height to the nearest tenth is 47.8 ft.
